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i^k 



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Terrestrial magnetism 
and atmospheric electricity 



Louis Agricola Bauer, John Adam Fie 




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TERRESTRIAL MAGNETISM 




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Terrestrial magnetism 

An International Quarterly Journal 



Edited by 

L. A. BAUER 

With the cooperation of the following Associates: 

C. Abbe, P. Baracchi, W. von Bezold, E. Biese, F. H. Bigelow, C. Borgen, C. Chistoni, 

W. DOBERCK, M. ESCHENHAGEN, J. HANN, G. HELLMANN, S. C. HEPITES,. D. A. GOLD- 

hammer, A. Lancaster, C. Lagrange, S. Lemstrom, G. W. Littlehales, 

J. Liznar, E. Mascart, T. C. Mendenhall, Th. Moureaux, G. Neu- 

mayer, F. E. Nipher, L. Palazzo, van Rijckevorsel, A. \V. 

Rucker, E. Schering, A. Schmidt (Gotha), C. A. 

Schott, A. Schuster, M. Snellen, E. Solander, 

I. P. van der Stok, R. F. Stupart, 

A. DE Tillo. H. Wild. 



"MAGNUS MAGNES IPSE EST GLOBUS TERRESTRIS " 

— Gilbert, ** Dc Magnete," 1600. 



VOLUME I. 

JANUARY- OCTOBER, 1896 



CHICAGO 

£t)e ©nibersttp of tft)irago tyxt## 

1896 



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TABLE OF CONTENTS 




GENERAL 

PAGE 

Allgemeiner Ausdruck fur die Coefficienten der Formel fur die 
Ablenkung einer Magnetnadel durch einen Ablenkungs- 
stab in beliebiger Lage C. Bbrgen 176 

A Summary of the Results of the Recent Magnetic Survey of 
Great Britain and Ireland conducted by Professors Rucker 

and Thorpe - A.W. Rucker 

I. On the Accuracy of the Delineation of the Terrestrial Isomagnetic 

Lines 105 

II. On the Accuracy of the Determination of the Local Disturbing 

Magnetic Forces 114 

III. On the Relation between the Magnetic and the Geological Con- 
stitution of Great Britain and Ireland 125 

Comparison of Magnetic Instruments Report of the B. A. A. S. Committee 72 

Die magnetischen Storungen der Jahre 1890-5, nach den Auf- 

zeichnungen des Magnetographen in Potsdam G. Liideling 147 

Die Vertheilung des erdmagnetischen Potentials in Bezug auf 

BELIEBIGE Durchmesser der Erde - Adolph Schmidt 18 

Editorial Greeting 41 

Halley's Earliest Equal Variation Chart. Reproduced in facsimile, 
for the first time, from a photograph furnished by Thos. Ward, Esq., of 
the chart in his possession. Text by - - - L. A. Bauer 28 

Isanomales et variations seculaires des composantes Y et X de la 

force magnetique horizontale pour l'epoque 1857 A. de Tillo - 163 

List of Associates 44, 104 

logarithmen der kugelfunctionen der ersten funf ordnungen 

von Funf zu Funf Grad .... - Adolph Schmidt 73 

On Electric Currents Induced by Rotating Magnets and their 
Application to some Phenomena of Terrestrial Magne- 
tism A. Shuster 1 

On the Distribution and the Secular Variation of Terrestrial 
Magnetism. No. IV: On the Component Fields of the Earth's 
Permanent Magnetism L. A. Bauer 169 

On the Existence of Vertical Earth - Air Electric Currents in 

the United Kingdom - - A. IV, Rucker 77 

The Secular Variation of the Direction of a Freely Suspended 
Magnetic Needle at Callao, Valparaiso, Shanghai, Hong- 
kong and Sydney - - • G. W. Littlehales 62 

Ueber Simultan-Beobachtungen erdmagnetischer Variationen 

M. Eschenhagen 55 

v 



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vi CONTENTS OF VOLUME I 

LETTERS TO EDITOR 

PAGE 

Magnetic Declinations Observed near the Spitsbergen Islands in 1894. A 

Report 0. B. French 85 

Magnetic Work in Australia - P. Baracchi 191 

Old Magnetic Declinations W. van Bemmelen 39 

Old Magnetic Declinations: The "Atfupcvperucri" - - G. Hellmann 153 
On the Best Form for the Components of Systems of Deflecting Forces. 

A Discussion • - - F. H. Bigelaw; Adolph Schmidt 32 

Some Observations of the Magnetic Inclination in China - W. Doberck 40 
Some Secular Variation Expressions of the Magnetic Declination 

G. W. Littlehales 89 

Ueber die Frage, in welcher Form die magnetischen Observatorien ihre 

Ergebnisse veroffentlichen sollen M. Eschenhagen 88 



NOTES 

Abstracts of Papers 94 

Action of Electric Currents on Mine-Surveying Instruments 155 L 

Cause of Delay of October Issue of Journal ..... 197 

/ Charles Chambers 154 

Der normale Erdmagnetismus ........ 158 

Deutsche Orthographie, by P. W. 1 56 

How Terrestrial Magnetism has been represented at some of the National 

Assemblies during the year 1895 4° - 

Magnetic Observations en route to Greenland - .... 197 

New Magnetic Observatories ........ 92 

Old Magnetic Declinations . . 87 

Old Observations of Magnetic Declination at Vienna • 157 

Personals and General 45, 90, 94, 154 

Simultaneous Observations of the Magnetic Perturbations ... 154 
The Construction of New Magnetic Charts of the Earth by the French 

Bureau of Longitudes 93 

The Financial Side of the Journai ... 92 
The Geologist's Interest in Terrestrial Magnetism ..... 91 
The International Meteorological Conference to be held in Paris in Sep- 
tember 1896 156 

The Magnetic Survey of Maryland ..... - 198 

The Necessity of a Magnetic Observatory at Melbourne 45 
What is Thought of Journal Terrestrial Magnetism - 90,91,92, 154 ) 



REVIEWS 

van Bemmelen, W.: Die erdmagnetische Nachstbrung F. //. Bigelow 53 
Carlheim-Gyllenskold, V.: Determination of the Magnetic Elements in 

Sweden ......... E. Solander 161 

Distribution of Magnetism in Southern Sweden E. Solander 200 



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CONTENTS OF VOLUME I vn 

PAGE 

Chree, C: Analysis of the Results of the Kew Observations - 

- - - W. van Bemmelen 95 

Comparison of the Magnetic Instruments in the Observatories of the British 

Isles G. W. LittUhales 200 

Creak, E. W.: The Magnetic Results of H. M. S. " Penguin," 1890-93 

G. W. LittUhales 199 

Fritsche, H.: Die magnetischen Lokalabweichungen bei Moskau und ihre 

Beziehungen zur dortigen Lokalattraction - - G. R. Putnam 50 

Liznar, J.: Die Vertheilung der erdmagnetischen Kraft in Osterreich- 

Ungarn zur Epoche 1890.0 - - - F. E. Nipher 49 

Palazzo, L.: Magnetic Observations in Italy - - - C. A. Schott 198 

Paulsen, A.: On the Nature and the Origin of the Aurora Borealis 

A. McAdie 1 59 

van Rijckevorsel: A Magnetic Survey of the Netherlands for the Epoch 

January 1, 1891 M. Eschenhagen 99 

Sella, A.: Sull' Intensita Orizzontale del Magnetismo Terrestre sul Monte 

Rosa P. W. 203 

Terrestrial Magnetism at the International Meteorological Congress, Chi- 
cago, 1893 - 102 

The Magnetic Observations made at the Observatory at Batavia C\ A. Schott 48 

The Potsdam Royal Magnetic Observatory - - - - L. A. Bauer 96 

Weyer, G. D. E.: The Magnetic Declination and its Secular Variation 

G. Herrle 162 



PUBLICATIONS 

Note 54 

List of - 103, 203, 204 



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TERRESTRIAL MAGNETISM 

AN INTERNATIONAL QUARTERLY JOURNAL 




volume i JANUARY, 1896 



ON ELECTRIC CURRENTS INDUCED BY ROTATING 
MAGNETS, AND THEIR APPLICATION TO SOME 
PHENOMENA OF TERRESTRIAL MAGNETISM. 

By Arthur Schuster, F.R.S., 
Professor of Physics at the Owens College, Manchester. 

Speculative theories on the magnetic and electric relation- 
ship between the Sun and Earth lack all solid basis, until we can 
give an answer to the question, whether interplanetary space is 
to be considered an electric conductor or not. The question is 
not one which can at present be touched by any argument as to 
the possible amount of matter which space may contain, for the 
behavior of gases in our vacuum tubes is so much affected by 
the dimensions of the electrodes and of the vessel, that no con- 
clusions can be drawn as to the electric behavior of molecules 
flying about in a boundless enclosure. 

It is my purpose to show how the behavior of the magnetic 
needle on the surface of the Earth may give us some information 
on the point. If it fails to do so it will be because the con- 
ductivity of space falls below a certain assignable value, and 
even that knowledge will be a gain. 

The Earth as a magnet revolving in a conducting medium, 
about an axis which does not coincide with its magnetic axis, 
must induce electric currents, which in their turn will produce 
certain magnetic and mechanical reactions. These reactions 
may be calculated and their existence tested within certain 
limits. 



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2 A. SCHUSTER [Vol. I, No. i] 

The distribution of electric currents in spherical conductors 
has been completely investigated independently by Professors 
Lamb and Niven, and special cases have been treated by Him- 
stedt, J. Larmor, and O. Heaviside. I am indebted to Professor 
Lamb for advice and help in the present investigation, in which 
I have endeavored to reduce the analytical processes to their 
simplest form, preserving at the same time the complete gener- 
ality of the solution. 

I consider then a magnetic system to revolve inside a spheri- 
cal cavity of a conducting medium. It may be imagined to be 
enclosed within a spherical surface concentric with the cavity, 
so that the space enclosed between the two surfaces is free of 
electric currents or magnetized matter. Nothing is lost by this 
assumption, as the two surfaces may in the limit be taken as 
coinciding. The magnetic potential outside the inner sphere I 
suppose to be expressed in a series of spherical harmonics. 

If referred to axes rotating with the Earth the two surface 
harmonics of type <r and order n may be represented with the 
usual notation by the real and imaginary part of 

where P n is the zonal harmonic of degree n, /* the cosine of the 
colatitude and A the longitude measured toward the east. 
Referred to axes fixed in space this term must be written 

^-^ l^r <* M = TV*-*, ( , ) 

where o> is the angular velocity of the Earth. In the outside 
medium the potential will therefore be represented by a series 
of terms like 

where 0_*_ x is the solid harmonic of degree — «— i. 

As there is now a factor containing the time, currents will be 
induced in space and each of the components of magnetic force 
a, b, c, say the first, must satisfy the equation 

d*a d'a d*a da 



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ELECTRIC CURRENTS INDUCED BY ROTA TING MAGNETS 3 



where * represents the conductivity of the medium. But as the 
magnetic forces are proportional to e~ ivmt y it follows that 



and hence 



da 



(V a + ?)« = o, 



« 



where y«=4iric<rW and v" denotes the usual operator. The other 
components of magnetic force satisfy the same equation, and 
there is the additional condition that 



da , db , dc 
dx^ dy^ dz 



(3) 



Assuming a uniform conductivity, the solution of the equation 
can be expressed in a series each term of which has the form 
ifr H (yr)$ H , r being the distance from the origin and <fr H a solid 
harmonic of degree n. Putting t=yr, the function $ n is defined by 

*,(0=(-)",. 3 . S . . . «M-,(j.J0"^. ( 4 ) 

The ambiguity in the sign of the power of the exponential is 
to be removed by the condition as to finiteness at infinity or at 
the origin. In our case we shall have to take e+%. 

The numerical factor is added to make the notation uniform 
with that of Professor Lamb, x who also gives the following 
relations, which are easily proved : 



*- = %= = ■ 



<* 



2n-\-i 



*.+ 



2«+I <% *" 



Ik— *«-«=; 



(5) 



(2«+l) (2«+3) 

When instead of <fr M we have a solid harmonic of degree 
— n — 1 we must define ^_-*_ x by • 

(— )- # ^ / 1 d v^* 



*-«(© = ■ 






1.3 .. . (2»— I) 

The three equations (5) hold for negative as well as for 

'Proceedings of the London Mathematical Society, Vol. XIII. 




4 A. SCHUSTER [vol. I. No. i] 

positive values of n. It will be noticed that +——, is equal to 
£"* + V« multiplied by a numerical factor which I designate by 
k n . It is seen that 

*=-=(a„ +3 )(a«+i). (6) 



It follows also from equations (5) that 



(7) 



We are now prepared to deal with the solution of our 
problem. 

In the space bounded by the revolving and fixed spheres 
there must be a magnetic potential of which one part Q.^, is 
due to the magnetic system and the other part X„, to the currents 
induced in the outer space. Continuous with the magnetic 
forces due to this potential we must in the outer space have 
forces which satisfy the equation (2) and therefore consist of 
terms having the form (3). We satisfy the conditions by put- 
ting in the conducting medium, apart from the time factor 

'=*~®% + *-J!0^ 1 (8) 

and in the cavity 

•=*«(«^+*-(«%^ (9) 

In these equations l = yr and £, = y R, where R is the radius 
of the cavity. The complete solution is derived by taking the 
sum of a series obtained by giving to n all values equal to or 
greater fhan unity. The equations for b and c are obtained by 
symmetry. The condition (3) applied to (8) and the two cor- 
responding ones gives, with the help of a well-known theorem 
relating to homogeneous functions, 

«*U *.-(* + i)^-.0— . = o, 
or with the help of (7) 

*+JCu + (* + 0* — . n-_. = o. 

fid ^' stand for ^(4) and ^'(&) respectively. This solves 
em, for it gives the ratio X n : O^^, and hence that of 
iced potential ^_ x (£,) X n to the inducing potential 



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ELECTRIC CURRENTS IND UCED BY ROTA TING MA GNETS 5 

We find 

Induced Potential __ — k M (n+ i) r ,+, ^,(t>) 

Inducing Potential /*^_*_.(£>) 

At the surface where { = £> 

and with the help of (6) 

It will be remembered that ^ = yR and / = 4n-#c<ra>/, hence 
4 = RV 2WK (TO) . (i + 1 ) = £(i + i ) . (u) 

As the \p functions occur in the expression for the magnetic 
forces in the outer space, they must vanish at infinity and this 
can only be secured by choosing the positive sign in the expo- 
nential of (4). 

The ratio of potentials at the surface may also be written 

1±-L *~ (12) 

where the argument of the function is fi(i + i). The ratio of 
the horizontal forces of the induced and inducing potential is 
also given by ( 10) , while the ratio of the vertical forces is simply 

A- <•» 

The ratio (12) will consist of a real and imaginary part and 
may be put into the form 

f>(cos<ra — /sin era) = E — t'F. 

The potential of the rotating magnets (see equation 1) was taken 
to be 

It follows that the induced potential will be 

which means that the potential and the horizontal forces are 
reduced in the ratio p : 1 and that there is an angular displace- 
ment a in the direction of rotation. The ratio (12) refers to the 
surface of the cavity; if the ratio of the potentials is required for 
any other distance, we must multiply by r : R v,+t . 




X 



6 A. SCHUSTER [Vol. I, No. ij 

Both the reduction in amplitude and the angular displacement 
are different for the different terms of the harmonic expansion. 
If a = o, that is for the zonal harmonics, there is no induced effect- 
at all. The leading term is therefore the one in which * = n = i. 
Putting n = i in ( I ) and substituting : 

*.«) = £, ^(i) = 3^ L: Y^, 

we obtain 

n+i Mi) = *e 

n *.«)-M0 C + yt-*' 

Here £ denotes its value at the surface which is fi(i -f- 1) and if 
the fraction is put into the form £ — iF 9 or p (cos a — i sin a) it is 
found that 



where 



*_---"', 


(14) 


„ 12/3-^+1) 

F N -' 


(15) 


^= 9 08+i)' + /3-(2i8+3)'. 






(16) 


3(i + 0) 
tan a = i* v , \ • 


(17) 



The expressions which are seen to be complicated in the. 
simplest case become more so when the harmonics of higher 
order are taken. By means of the following equations, the 
results may be calculated in every case. Let the inducing 
potential be a solid harmonic of degree — n — 1 , and put 

4'- T («-3)(«-4) (»0) 4 1 (—5) («~6) (»-7) (»-8) (ag)» /.ox 

yX -- 1 (a*- 3 ) (a«- 5 ) 4! "*" (a«~3) («*-5) (a*~7) (»*"9) »! ' '* V ' 

J'=R- -5Z1 ?*! _ ( W - 4 ) («- 5 ) a40« (»- 5 ) („-6) (»- 7 ) a«£ . , v 

-"•-P a«- 3 3! (a«- 3 )(a«-5) 5* "^ (a«"3) <t«-s) (»*-7) 7* " " * V *' 

«' = ^Zl^ _ (»-4)(n-s)(«-6) (»fl) 6 , (»-6) („- 7 )(„-8) («- 9 ) («-,o) (afl 10 
" ~ a»-3 al (aw— 3) (a*— 5) (an— 7) 6! ' (a* — 3)(»*-5)( 2 * — 7)( a *~ 9)( 2 * — «) "> ! 

— . . . . (20) 
/?• = fl 4. "-3 22! (— 4)(— S) *P $ (n-$) (n-6) (h- 7 ) ag_* ■ , * 

-°--P T «,- 3 3! * (a*-3) (»*-5) 5! (a*-3) l»«-5) («*-7) 7!+ "*" ' * * * l ' 

In the series for A' m and /?„ the sign is alternately positive 
and negative, while in the two other series each sign is twice 
repeated, with the exception of the first positive sign in the 



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ELECTRIC CURRENTS INDUCED BY ROTA TING MAGNETS 7 

series for A' M . Each series breaks off when one of the factors 

vanishes or becomes negative. The case n = I has been treated 

already and is not included in the general expression. If we 

now write 

A U = A' U + A' m B H = B' H + B' ut 

tanO n = -f- % <T<Ln = n —0 H + % —- 9 (22) 

A m 2 

it may be shown that the ratio p of the induced to the inducing 
potential as regards magnitude is 

and that the angular displacement in the direction of rotation 
is a„. 

So far we have only treated of the magnetic reactions which 
are due to the currents induced in the outer medium. The 
currents u t v, w themselves are easily written down by means 
of the well-known relations 

dc db 
* U = lTy—d-z- 

After a few simple transformations we find thus 

with similar equations for the two other current components 
v and w. 

We are now prepared to discuss the mechanical effects. It 
is clear from considerations derived from the principle of the 
conservation of energy, that the currents induced by a magnet 
rotating in a cavity of a conducting medium must tend to 
diminish the kinetic energy of the rotating body ; but whether 
the forces resolve themselves only into a couple, diminishing 
the angular velocity, or whether the axis of rotation itself tends 
to be displaced, can only be determined by analysis. The 
result is arrived at most quickly by means of the principle of 
work. The external action of the magnetized sphere is the 
same as if it were covered with magnetic matter of density s. 
If the magnetic potential due to the external forces is V, the 



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8 A. SCHUSTER [Vol. I. No. i] 

work which would ha z to be done by these forces in bringing 
the magnetic matter into its position from an infinite distance 
without altering the relative distribution of s over the sphere, is 



/ 



VsdS, 



where the integration is to be taken over the spherical surface. 
If we imagine an angular displacement d<f> about any axis OK, 
and express the additional work done, we find that the couple 
opposing the rotation is given by 



/ 



•%« 



The surface distribution s on a sphere of radius R is obtained 
for each term of the harmonic expansion by 

if 0__, denotes its value at the surface of the sphere. 

The only part of V which gives a finite value when the 
products are integrated over the sphere is 

Xu = Pm (cos a„ — /sin aj Cl^_ s , 

X n denoting the induced potential at the surface of the sphere. 
If the couple about the axis of rotation is required, //<£ = <&, 
and for the term 

we have 

Hence the couple L is determined by 

L = ^±^lj [i p (cos a - /sin a) G_„_,] [O...J dS, 

where the real parts of the expressions included in square 
brackets must be taken before multiplication. By means of the 
well-known value of the surface integral of the square of a 
tesseral harmonic it is thus found that to a term in the revolving 
potential expressed by 

Tf cos <r (X — t*t) 
there corresponds a couple opposing the rotation equal to 



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ELECTRIC CURRENTS IND UCED BY £ TA TING MA GNETS 9 

<r (n -\- a) ! .-> < 

- ^ ; ! r~. Pn Sin a H . 

2R*" + X (fi — <r)r M 
If n = <r= I, 

psina /? 



L = 



R 3 R 3 



the value of E being that given in (14). 

If the sphere is magnetized uniformly along an axis forming 
an angle ^ with the axis of rotation and / denote the magnetic 
moment 

Z = *£**. (*4) 

The other component of the couple is more difficult to 

calculate in the most general case, and I confine myself to the 

statement of the result when the magnetization is uniform and 

defined as before by the two quantities / and ^. The second 

couple which, together with Z, makes up the whole mechanical 

effect, is then given by 

._ (/"psin^cos^) 

M = jp • 

Its axis is at right angles to the axis of rotation in such a 
way that the plane containing the axis of L and M forms an 
angle a with the plane containing the axis of rotation and the 
direction of magnetization. 

We are now prepared to deal with the special application of 
our problem to the earth rotating in a medium having possibly 
an electric conductivity. It will be sufficient for our purpose to 
consider the earth as a homogeneously magnetized sphere. The 
earth's potential in space would be represented by 

Iz ' t \ 

— ' ( 2 5) 

if z' is measured along the magnetic axis. When resolved along 
the axis of rotation, and taking the axis of x to lie in the plane 
containing z and z\ the potential takes the form 

Hz cos *lt+x sin^) 

or by transforming to polar coordinates 

7(cos^ cos + sin ^ si ng cosX) . * 



IO 



A. SCHUSTER 



[Vol. I, No. i] 



where $ denotes the colatitude, A the longitude measured from 
the meridian which is drawn through the magnetic axis and / is 
the magnetic moment of the earth, which, for our purpose may 
with sufficient accuracy be taken in e.g. s. units as equal to 
0.33 X (earth's radius) 3 . 

From (24) it appears that for a homogeneously magnetized 
sphere the retarding couple is proportional to 

9(^+1) +^(2^ + 3) K7) 

The value of fi is given by (11), where now we must put 
9=1. In the accompanying table the first column gives the 
value of fi, the second column the corresponding conductivity 
* after multiplication by 10 16 . The angular velocity and radius 
are taken to be equal to those of the Earth for which 
2v R = 4X io 9 , 2v:u> = 86400 and hence, 1 : 2 wvR* = 54 X io~ 16 . 

The third and fourth columns give the values of p and a 
defined by (16) and (17), and the last two columns give the 
quantities E—p cos a and F=p sin a. 

ft io x6 k p a 2s=/>cosa /=/>sin a 



0.1 


O.54 


0.0121 


84° 


27' 


0.0012 


0.0119 


0.2 


2.16 


0.0437 


79 


18 


0.0081 


0.0428 


0.3 


4.86 


0.0890 


74 


3i 


0.0237 


0.0857 


O.4 


8.64 


0.1433 


70 


06 


0.0486 


0.1344 


0.5 


13.50 


0.2076 


69 


06 


0.0740 


0.1933 


0.6 


19.44 


0.2657 


62 


18 


0.1232 


0.2345 


0.7 


26.46 


0.3292 


58 


52 


0.1701 


0.2825 


0.8 


34.56 


0.3917 


55 


44 


0.2207 


0.3238 


0.9 


4374 


0.4533 


52 


50 


0.2736 


0.3606 


1.0 


54.00 


0.5123 


50 


12 


0.3277 


0.3932 


2.0 


21.6 Xio 


0.9614 


32 


44 


0.8082 


0.5199 


2.II88 


24.24X10 


0.9996 


3i 


23 


0.8521 


0.5206 


10 


5-4 Xio 9 


1.722 


8 


10 


1.703 


2442 


5x10 


135 XI03 


1. 94 1 


1 


42 


1.940 


0.0574 


I0 a 


54 Xio* 


1.97 1 





51 


1.97 1 


0.0292 


103 


54 X io« 


1-997 





05 


1.997 


0.0029 



It appears that F vanishes both for an infinitely great and 
infinitely small conductivity ; that is to say there is no couple 
tending to retard the Earth's motion when either the conductivity 
or resistance is infinite. The fact that a sphere transversely 
magnetized may rotate in a medium of infinite conductivity 
without retardation appears surprising at first sight, but it may 
be pointed out, that a similar result has been obtained by Max- 
well for a magnetic pole moving parallel to a conducting sheet 



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ELECTRIC CURRENTS INDUCED BY ROTA TING MAGNETS 1 1 

{Electricity and Magnetism Vol. II., p. 275, 2d edition). The 
explanation lies in the circumstance that the currents induced in 
a conductor of infinite conductivity are confined to an infinitely 
thin layer at the surface ; as the currents do not become infinitely 
great the total work done vanishes. 

The table shows that the retarding couple increases with 
decreasing conductivity to a maximum and then diminishes again. 
The maximum of i^may be obtained from the expression (27). 
The numerical calculation gives at the maximum 

P= 2.1 18784, 
k = 2.42 x icr u . 

I have calculated this value of P which gives the maximum 
retarding couple to more decimal places than would have been 
necessary, but this was done in order to satisfy myself of the 
accidental nature of a very curious coincidence. Reference to 
the table or to the equations shows that the value of p, which is 
the ratio of the induced to the inducing potential approaches the 
number 2 for high conductivities. There is, therefore, one con- 
ductivity for which the two potentials are equal, and a first 
approximation showed that this conductivity was numerically 
equal to that which gives the maximum retarding couple. The 
mathematical conditions were quite different in the two cases, yet 
both led to a value of p = 2.12 apparently. Pushing the calcu- 
lations to a higher degree of accuracy I found that the value of 

P which gives p = 1 is 

P= 2.120006 

The two numbers differ by about one part in 2000, but the 
coincidence is accidental. 

The table shows that if the conductivity is about io~~ xo e.g. s, 
units, the effects are practically the same as if the conductivity 
were infinitely great. The conductivity of mercury being about 
io"" 5 , it appears that both mechanical and magnetic reactions of 
electric currents induced in space are practically the same for any 
conductivity lying between infinity and one which is 100,000 times 
smaller than that of mercury. The maximum retarding couple 
would be experienced, for a conductivity which we should con- 
sider an exceedingly small one compared to that of ordinary con- 
ductors being 2.4 Xio" 9 that of mercury. 



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1 2 A. SCHUSTER [Vol. I, No. ij 

As regards the magnitude of the retarding couple, we may 
easily calculate its effects. If AfK* is the moment of inertia of 
the sphere and • its angular velocity 

d <i> 

and hence by the ordinary process of solution, if <* be the angu- 
lar velocity for / = o 

tat AfK't* 
*> t — u>~ L ' 
where 

L - ^ " 
The numerical value of F sls shown in the table is 0.521. 
Also / : R* = 0.33 and sin 9 ^ = 0.144, 

Hence Z = 0.00818^ and MK* *> : Z = 3.42 X io rt . 

In a time T the angular velocity of the Earth would thus be 
reduced by an amount which is given by 

0) ftf T _^ 

to 3.42 X io' 4 

It is seen that it would take 125 centuries to lengthen the 
day by one second. Small as this effect seems to be it could 
not have escaped the notice of astronomers, for the Earth as a 
timekeeper would lose 2.6 minutes in a century ; roughly speak- 
ing this would be about seven times the amount calculated by 
Professor G. Darwin for the effect of tidal friction. Considering the 
uncertainties of the lunar acceleration, and the causes which tend 
to retard and accelerate the Earth's rotation I think it may safely 
be asserted that a loss of four seconds of time in the century 
could not be disentangled from the variations due to other causes. 
This would limit us to a possible couple about six times smaller 
than the maximum, and hence if space had a conductivity either 
smaller than 5 X io"" 16 or greater than 10"" the effects as 
regards the lengthening of the day would be inappreciable. 

The magnetic effects of the induced currents are completely 
defined by (12) and (13). 

If the conductivity is great it is easily shown that 



*-.-*. 



= 1. 



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ELECTRIC CURRENTS INDUCED BY ROTA TING MA GNETS 1 3 

Hence the horizontal forces on the surface of the Earth due to 
the induced currents are n ~ times greater than those due to the 
inducing forces, and the induced vertical force is equal and oppo- 
site to the inducing force. The magnetic forces on the surface 
of the Earth rotating in a medium supposed to conduct suffi- 
ciently well, would be distributed in a way which might well have 
puzzled magneticians. There would be no vertical force, but 
the declination would be increased everywhere. The agonic 
lines would be the same as now. Considering the Earth as a 
uniformly magnetized sphere (w = i), the tangent of the declina- 
tion would everywhere be twice what it is at present. If this 
conductivity of space though small is appreciable, the induced 
forces are obtained in the following way : Let the Earth's poten- 
tial referred to its geographical axis be given by the expression 

(26) or 

(cos ^ cos + sin ^ sin cos A) 

4/ — •_/ _^__ ___^^__^__^_______^___^__ 

r a 
then the induced potential is given by 

X = /sin \ff sin (E cos \ + Fsin \) = /sin ij/ sin Op cos (k — a). 

The values of E and F (or if preferred of p and a) which 
correspond to a given conductivity *, may be found by reference 
to the table. Now the analysis of Gauss allows us to separate 
the inside from the outside forces and we may perhaps hope 
that within a comparatively short time we may have sufficient 
information to fix the outside forces for the leading terms to 
within a few per cent. In that case a conductivity of space equal 
to io~" 16 c. g. s. units could be detected. 

Our calculation has proceeded on the assumption of a uniform 
conductivity of space, but it may be seen from general considera- 
tions that the principal effects would be the same, even if the 
assumption does not hold. We may be wrong as regards the 
numerical estimate of the conductivity which produces a certain 
effect if that conductivity varies, but however unequal the elec- 
tric resistance of different portions of space may be, the reactions 
must always be such as to cause an induced potential displaced 
in the direction of the rotation as compared to the inducing one. 

We have also not considered some very important effects 
which may be due to currents induced in the meridian planes 



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14 A. SCHUSTER [Vol. I. No. ij 

near the limits of our atmosphere. Such currents, it is easy to 
see, might produce effects similar to that of the aurora, but I 
must for the present postpone their discussion. 

It is very tempting to enter into more speculative ground and 
to ask ourselves the question, how would the induced magnetic 
forces react on the earth's magnetic system. The reply must 
depend on the ideas we have formed as to the actual causes 
which produce terrestrial magnetism and I will therefore only 
answer it in a perfectly hypothetical and abstract case. 

Imagine a rigid system of magnets embedded inside a sphere 
by means of a substance which at first is assumed to be abso- 
lutely rigid. Let the sphere be set into rotation in a conducting 
medium, and consider the magnetic forces which will act on the 
sphere. If OP be the magnetic axis and ON the axis of rota- 
tion, then our previous results show that a transverse magnetic 
force will be generated which can be decomposed into two, one 
of which would tend to magnetize the sphere along an axis at right 
angles to Of* and ON, while the other would tend to shift the mag- 
netic axis from OP towards ON. The combined effect will be 
a tendency to shift the magnetic axis, in a direction opposite that 
of the sphere's rotation, round the axis of rotation and at the 
same time towards it. Whether an actual shifting of the mag- 
netic axis would be produced depends on the magnetic proper- 
ties of the material. If there is any magnetic yielding as there 
is a yielding in solids to steadily applied forces, the magnetic 
axis would be made to revolve slowly and steadily in a spiral 
curve round and towards the axis of rotation, the direction of 
rotation of the axis being opposite to that of the impressed 
rotation of the sphere, i. e. t from east to west in the case of the 
Earth. 

If we now imagine the medium which holds the magnetic 
system to be itself yielding in a manner shown in an exaggerated 
form by cobbler's wax, there will be a further tendency for the 
whole magnetic system to move within the sphere, and here 
again a displacement of the magnetic axis would take place iden- 
tical with the one just indicated. In whatever way the sphere 
was originally magnetized, the magnetic axis and the axis of 
rotation would ultimately tend to coincide. 



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ELECTRIC CURRENTS INDUCED BY ROTA TING MA GNETS 1 5 

We know nothing of the magnetic interior of the inside of 
the Earth, but we may assert that if there exists any analogy 
between the condition of that interior and the concrete case of 
a magnetic system embedded inside a sphere, and yielding 
either magnetically or bodily, and if the interstellar space 
behaves like a conducting medium, a change in the Earth's 
magnetic axis would result, causing changes in the magnetic 
forces which are identical with those actually observed in the 
secular variation. 

That the secular variation of terrestrial magnetism may be 
accounted for by the rotation of a magnetic system inside the 
Earth has often been suggested and was illustrated in an inter- 
esting manner by Mr. Henry Wilde with the help of his Magne- 
tarium. Dr. Bauer has moreover recently proved that magnetic 
observations taken during the past century are sufficient to show 
a displacement of the magnetic axis in the Earth, the direction 
of the displacement being in agreement with the theory indicated 
above. In interpreting Dr. Bauer's work it must be remembered 
that the theory of spherical harmonics shows that any magnetic 
system whatever may be decomposed into two, one of which is 
equivalent to a magnetization along an arbitrarily chosen axis 
and the other at right angles to it. When treating of the mag- 
netic forces on the surface of the Earth, it is convenient but not 
necessary to take the axis of rotation as axis of reference, and 
the secondary poles which appear in Dr. Bauer's papers are con- 
sequences of this particular method of decomposition. The dis- 
placement of the Earth's magnetic axis implies the displacement 
of the secondary poles, and vice versa. Whether these secon- 
dary poles have any real existence or not depends on the views 
we may have formed as to the causes of terrestrial magnetism, 
but in the first instance they appear as a consequence of a par- 
ticular choice of coordinate axes. I take this opportunity to 
add the remark that Dr. Bauer's method seems to me to be the 
one best adapted to bring out the principal facts of the secular 
variation in a mathematical form. If our data were sufficient 
the vertical force might with advantage be taken as the basis of 
investigation instead of the angle of dip, for the lines of equal 
vertical force are very nearly the same as the equipotential lines, 



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1 6 A.SCHUSTER [Vol. I, No. i] 

while Dr. Bauer's method suffers from the disadvantage that the 
angle of dip of a combined field cannot be obtained from the 
angles of the two separate fields. His curves do not represent 
therefore the dip which would be produced by what he calls the 
secondary field. I am aware, of course, of the practical difficulty 
due to our insufficient knowledge of vertical forces which, no 
doubt, has obliged Dr. Bauer to select the dip angle, but it is to 
be hoped that this difficulty may soon disappear. 

The problem treated in these pages having opened out tl.e 
possibility of an explanation of the secular variation, it is neces- 
sary to turn to such observational evidence as may be at our 
disposal for confirmation or refutation of the suggested ideas. 
While I am writing this paragraph, I receive by post the full 
results of Dr. Adolf Schmidt's recent calculations, in which for 
the first time the outside magnetic potential at the surface of the 
Earth has been separated from that due to inside causes. An 
abstract of the work had been communicated to the meeting of 
the British Association at Oxford and his principal results had 
been familiar to me. If we could adopt Dr. Schmidt's numbers 
as final, they would show that the outside magnetic potential is 
displaced towards the east. Such an effect might be produced 
by currents induced in a medium rotating more rapidly than the 
Earth, which might be the case if the upper currents of the 
atmosphere had a general drift from west to east. The dis- 
placement of the outside potential, according to Dr. Schmidt, is, 
however, greater than 90 , which is difficult to reconcile with the 
hypothesis of induced currents under any circumstances. It 
must be remembered that whatever these outside forces are due 
to, the forces and therefore their cause rotates with the 
Earth, and if Dr. Schmidt's numbers are correct, we should have 
to look for some supply of energy from the outside tending to 
accelerate the Earth's rotation. From communication with Dr. 
Schmidt, as well as from the carefully guarded statements in his 
published work, I judge that he does not wish to put forward 
his numbers in any way as finally conclusive. His method of 
computation is a great advance of our previous knowledge, but 
I think may in certain points be improved upon. I hope before 
long to be able to give the results of a renewed calculation based 



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ELECTRIC CURRENTS INDUCED BY ROTA TING MAGNETS 1 7 

on fresh material and having for its object to calculate with 
special accuracy the two leading terms in the series of spherical 
harmonics. Should Dr. Schmidt's numbers be then confirmed 
and the outside forces be shown to act in such a way that they 
tend to displace the Earth's magnetic axis in the direction of its 
rotation, it would be conclusively proved that the secular varia- 
tion cannot be due to outside forces. 



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DIE VERTEILUNG DES ERDMAGNETISCHEN POTEN- 
TIALS IN BEZUG AUF BELIEBIGE 
DURCHMESSER DER ERDE. 

Von Db. Ad. Schmidt (gotha). 

In einem vor drei Jahren gehaltenen, im verflossenen Fruh- 
jahre veroffentlichten Vortrage x hat Herr von Bezold darauf 
aufmerksam gemacht, dass die Mittelwerte, die das magnetische 
Potential auf den einzelnen Parallelkreisen annimmt, mit sehr 
grosser Annaherung dem Sinus der geographishen Breite /8 f 
anders ausgedruckt dem Cosinus des Nordpolabstandes u propor- 
tional verlaufen. Indem er namlich die Gesamtheit dieser Mittel- 
werte, das von ihm sogenannte normale Potential, mit V H , die 
Abweichungen von diesem mit V m bezeichnet, so dass das ganze 
Potential V durch die Gleichung 

V=Vu+V. 

bestimmt wird, findet er, dass mit R als dem Erdradius fast 
genau 

zu setzen ist. Auf der Grundlage der von Quintus Icilius 
gezeichneten Karte des Potentials fur die Epoche 1 880,0 ergiebt 
sich ihm K gleich 0,330 cntr^ g* j~ x , wahrend die mittlere 
Abweichung der Function Ks\xi$ von V n : R nicht gr6sser als 
±: 0,0029 ctnr* g*s~ z wird. 

Es liegt die Frage nahe, ob die Rotationsaxe der Erde in 
dieser Hinsicht vor ihren ubrigen Durchmessern ausgezeichnet ist 
oder ob etwa bei einem unter diesen die entsprechend gebildeten 
Abweichungen noch geringer ausfallen. Mit Rucksicht auf die 
verschiedentlich, vor allem auch in der genannten Abhandlung 
bemerkte M6glichkeit eines Zusammenhangs der erdmagnetischen 
Erscheinungen mit der Rotation der Erde kann eine exacte 

1 Ueber Isanomalen des erdmagnetischen Potentials. Sittungs-Berichte der 
Akademuder Wisscnschaften zu Berlin; math.-phys. Ctasse, 1895, P a g« 363-378. 

18 



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VERTEILUNG DES ERDMAGNETISCHEN POTENTIALS 1 9 

Beantwortung dieser Frage, gleichgiiltig, in welchem Sinne sie 
auch ausfallen mag, einiges Interesse beanspruchen. 

Urn die Aufgabe scharfer zu formulieren, denke ich mir das 
Potential nach Kugelfunctionen entwickelt. Es sei 

V=R^ 2 K ( cos *) [ G l cos « X + ffZ sin m x] 

W-I JW-O 

V n enthalt dann diejenigen Glieder, die von der geographi- 
schen Lange k unabhangig sind, in denen also m = o ist, wahrend 
V a von alien iibrigen Gliedern gebildet wird. Der Satz, dass V u 
sehr nahe durch ATsin0 (oder ATcosa) wiedergegeben wird, ist 
ein Ausdruck der Thatsache, die sich aus den weiterhin mit- 
geteilten Zahlen (S. 2i) ablesen lasst, dass unter den Coeffici 
enten G% der erste, G] (=AT),alle iibrigen betrachtlich ubertrifft. 

In nunmehr leicht verstandlicher Abkiirzung will ich noch 

r.J? = /Ccos u+/(u) + <f> (u, \) 
setzen. Es ist dann 

V n = R(K cos m+f {$$)), V m = R . * («, X). 

Nun kann man auch fur jeden von der Rotationsaxe der Erde 
verschiedenen Durchmesser ein den Breitenkreisen und Meri- 
dianen analoges Liniensystem entwerfen. An Stelle der gewohn- 
lichen geographishen Coordinaten fi, k oder u, k treten dann 
andere fi' , k' oderj*/, k\ und indem man das Potential in Bezug 
auf das neue System in gleicher Weise zerlegt, wie es soeben im 
alten geschehen ist, erhalt man 

Die Frage, die uns hier beschaftigen soil, lasst sich dann kurz 
so formulieren: Fur welchen Durchmesser der Erde ist f x (u') 
in der Gesamtheit seiner Werte auf der ganzen Erde ein Mini- 
mum ? Als charakteristischer Ausdruck fur das, was ich hier die 
Gesamtheit seiner Werte nenne, kann wohl nichts anderes als 
das fiber die ganze Erdoberflache genommene Integral 

gelten, in dem du> das Flachenelement bezeichnet. Dieses 
Integral ist gleich 4 *■ F, wenn F der (quadratische) Mittelwert 
von /,(«') auf der Kugelflache ist. 



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20 A. SCHMIDT [Vol. I, No. ij 

Man kdnnte die entsprechende Erage in Bezug auf /, (u') + 
<f>t (*',X') stellen. Die Antwort ist hier sofort gegeben. Diese 
Grdsse ist offenbar in dem soeben angegebenen Sinne ein Mini- 
mum, wenn K x cos u' sein Maximum erreicht, was bei der mag- 
netischen Axe der Erde zutrifft. Fur jeden Durchmesser, der 
mit dieser den Winkel a bildet, ist ja K x — M cos a, wenn M das 
magnetische Moment bedeutet. 

Zur ersten Frage zuriickkehrend, fiihre ich zunachst eine etwas 
geanderte Bezeichnung ein, die wesentlich zur Vereinfachung der 
folgenden Entwickelung beitragt. An die Stelle der Functionen 
PZ lasse ich durch Hinzufugung passender constanter Factoren 
andere Functionen R" m treten, die so gewahlt sind, dass fur jeden 
Wert von n und m der Ausdruck R* m cos mX und, ausser fur 
m = 0, auch RZsinmX auf der Kugelflache den Mittelwert I 
besitzt. Wie man leicht ubersieht, erreicht man dies durch die 
Substitution 



R n = A( 2 n^-i)a n P*- J €{2 - n ^- l) M^^}} T n 

mit n [1.3. 5. . . (2 n— 1)]2 d <=i fur m = o 

a *« * (n—m)\(n + m)\ « = a fur w > o 

Das Potential erscheint dementsprechend in der Form 
V= R V V R M m (cos u) [gZ cos m X + A* sin m X] 

wobei X die von Greenwich nach Osten gezahlte geographische 
Lange bedeuten soil. Mit Rucksicht auf das Folgende fuhre 
ich noch eine Abkurzung ein, indem ich 

R n (cos u) coswX = ^ , R" (cos u) sin m\ = s" 

setze ; es wird dadurch in vereinfachter Schreibweise 

(x) v=R ^n ^~(gz*z+* M m s z)- 

Fur die Coefficienten g und h wahle ich die von mir aus Dr 
Neumayer's Werten der erdmagnetischen Elemente fur 1885,0 
berechneten (mit n = 6 f m = 4 abbrechenden) Zahlen, x die in der 
Einheit cnc* g* sr l folgendermassen lauten : 

1 Diese Zahlen sind allerdings unter Beriicksichtigung der Abplattung der Erde 
berechnet worden, die ich hier, um die Entwickelungen nicht zu complicieren, ausser 



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VER TEIL UNG DES ERDMA GNETISCHEN PO TENTIALS 2 1 



ft 


i 


2 


3 


4 


5 


6 


*: 


—0,18322 


—0,00234 


0,00354 


0,00265 


— 0,00051 


0,00006 


t? 


— 0,01360 


0,01264 


—0,00466 


0,00171 


0,00119 


0,00006 


A' 

I 


0,03455 


— 0,00321 


— 0,00112 


0,00095 


— 0,00081 


0,00025 


*." 




0,00303 


0,00540 


0,00172 


0,00086 


—0,00015 


£ 




0,00689 


0,00010 


— 0,00057 


— 0,00010 


0,00018 


M 

?3 






0,00151 


— 0,00103 


0,00005 


—0,00045 


*; 






0,00258 


—0,00075 


0,00007 


— 0,000 % 8 


<r 








0,00053 


— 0,00002 


— 0,00006 


-c 








—0,00025 


— 0,00023 


—0,00007 



Das Vorzeichen des Potentials ist hier entsprechend dem 
Gebrauche, der sich in der theoretischen Physik langst einge- 
burgert hat, so gewahlt, dass die Richtung der auf den Nordpol 
einer Magnetnadel wirkenden Kraft mit der Richtung abneh- 
mender Potentialwerte iibereinstimmt. 

Die LSsung unserer Aufgabe erfordert nun nichts als eine 
Coordinatentransformation, durch welche der fur V angegebene 
Ausdruck (1) in die Form 

ubergeht, worin entsprechend der zuvor eingefuhrten Abkurzung 
R* (cos u') cos m A/ = y*, R" (cos u') sin m \' = <r n 

wit » ' * wrt wH x ' twt 

gesetzt ist. Nach Ausfuhrung dieser Transformation hat man 
den fruheren Betrachtungen zufolge den Mittelwert von/ (#'), 
d. i. von (jl H+Jl y* + . . . ) zu bilden. Mit Rucksicht auf die 
bekannten Eigenschaften der Kugelfunctionen und auf die 
Definition der RZ ist das Quadrat dieses Mittelwertes offenbar 
(3) W=JUl+JlJl + 

so dass nur die Berechnung der Coefficienten/; erforderlich ist. 
Es sei nun N' , der Pol des neuen Systems, im alten, dessen 
Pol N heissen soil, durch die Coordinaten u , \, definiert. Sein 
Anfangsmeridian gehe durch N, und die Zahlung der Lange (A/) 
erfolge in ihm im umgekehrten Sinne wie im alten (bei k). 
Die in beiden Systemen bestimmten Coordinaten u 9 k und u' , k' 

Acht lasse. Die Ungenauigkeit, die dadurch entsteht, dass ich sie hier als auf die 
Kugel beziiglich einfiihre, ist von derselben Grossenordnung wie die durch die Ver- 
nachlassigung der Abplattung bewirkte und ist wie diese fiir den vorliegenden 
Zweck vollkommen bedeutungslos. 




^g^e^ 



22 A. SCHMIDT [Vol. I, No. ij 

irgend eines Punktes P der Erdoberfl&che sind dann mit den 
Seiten und Innenwinkeln des spharischen Dreiecks PNN' durch 
die Beziehungen verbunden : 

NN' = u 09 NP= u, N'P= u' f N'JVP=k—\ oi NN'P= X' 

Setze ich zun&chst zur Vereinfachung Xo=o f so ist offenbar 
die Beziehung zwischen beiden Systemen eine symmetrische oder 
reciproke; das eine geht aus dem andern auf dieselbe Weise 
hervor wie dieses aus jenem. Die Transformationsgleichungen, 
welche die Functionen y, a mit c, s verbinden und die, wie man 
aus der Theorie der Kugelfunctionen weiss, homogen und linear 
sind, bleiben mit andern Worten gultig, wenn gleichzeitig y mit c 
und <r mit s vertauscht wird. Ueberdies schliesst man leicht aus 
der geometrisch evidenten Thatsache, dass fur \,=o die Ver- 
tauschung von X mit — X bei unge&ndertem u auch u\ X' in 
«', — X' uberfuhrt, dass die yi allein von den r* und die <r£ 
allein von den s£ abh&ngen; denn diese beiden sind ungerade, jene 
gerade Functionen von X oder X'. Da wir nun von den in (2) 
auftretenden Coefficienten nur die der Functionen y gebrauchen, 
so genugt die Betrachtung desjenigen Systems von Gleichungen, 
das zwischen diesen und den Functionen c besteht. Nach dem 
Gesagten muss sich dieses System gleichzeitig in den beiden 
Formen 

( 4 a,b) y*=]T' *„,;;?, C=2' "*"<*' (m = o,i,2 . . . n) 

darstellen lassen, wobei das Summenzeichen ebenso wie uberall 
in der Folge eine Summation von bis zu dem festen Werte n 
bezeichnet. 

Es sei nun A die Determinante der zu bestimmenden Coeffi- 
cienten a^ , und a mi bezeichne die zu a mi gehSrige Adjuncte 
oder Unterdeterminante. Die Auflosung der Gleichungen (4a) 
ergiebt dann 

*■ ? = — 7 m a .y* oder C n = — 7 ' a . v* . 
* A / j mi 'm v " w * m ^ / { «• ' « 

Diese Losung muss mit dem Gleichungssysteme (4b) uberein- 
stimmen, woraus sich sofort die fur alle Werte der Indices giil- 

tige Beziehung 

1 



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VER TEIL UNG DES ERDMA GNETISCHEN POTENTIALS 2 3 

ergiebt. Fiihrt man diese in die bekannten Grundgleichungen 
der Determinantentheorie 

/* a im *,** = *, 2J a ik * im = o fur k^m 

ein, so erhalt man, wenn k und m wieder verschiedene Indices 
sind 

(5) 2^J a,m ami= *> 2' aik <*>*'= °> 

woraus nebenbei mit Riicksicht auf die Festsetzung iiber den 
Drehungssinn von A und A' abgeleitet werden kann, dass A =- 1 
ist. 

Werden andrerseits die Gleichungen (4a) oder (4b) qua- 
driert als auch zu je zweien miteinander multipliciert, und wird 
dann auf beiden Seiten uber die ganze Kugelflache integriert, so 
folgt vermdge der durch die Definition der Functionen R%, 
bedingten Beziehungen 

dass allgemein 

(6) ?* a mi a mi = 1, ?* a ki a mi —o 

sein muss. Hieraus in Verbindung mit (5) ergiebt sich, dass 
fur jeden Wert von k, k=m eingeschlossen, 

7^ '' a m i {<*ik — a hi ) = o 

ist. Fur einen bestimmten Wert von k und fur w=o,i,2 . . . . n 
liefert dies ein mit (4) in alien Coefficienten ubereinstimmendes 
System von (/1+1) unabhangigen Gleichungen, dessen Losung 

(7) a. A -a k .=o oder a a = a„ 

lautet. (Eine der (/i-fi) Differenzen verschwindet offenbar 
identisch, so dass man eigentlich nur n Gleichungen in Betracht 
zu ziehen brauchte. Der Beweis wird aber dadurch nicht ver- 
einfacht, sondern erschwert, da man erst nachweisen musste, dass 
die Determinante der n Gleichungen, d. i. a kkf von Null verschieden 
ist.) 

Der hiermit gefuhrte Nachweiss, dass die Determinante der 
Transformationsgleichungen (4) symmetrisch ist — ein Vorteil, 
der der Einfiihrung der Functionen /?* verdankt wird — macht 



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24 A. SCHMIDT [vol. I. No. i] 

die zwar nicht schwierige, aber etwas umstandliche Aufstellung 
dieser Gleichungen fur unseren Zweck uberflussig. Fuhren wir 
namlich die Umwandlung der Form ( I ) des Potentials V in die 
Form (2) mittels der in (4b) angegebenen Substitution wirklich 
aus, so erhalten wir sofort 

und dafur wurden wir nunmehr 

(8) >:-2"*«'- 

schreiben. Die hierin auftretenden Coefficienten a om ergeben 
sich leicht aus einer bekannten Fundamentalgleichung der Theorie 
der Kugelfunctionen. Es ist ja im Dreieck PNN' 

cos u' = cos u cos u -f sin u sin u cos k 
und daher nach jener Gleichung 

^7 P*(cosu')=P H (cos u')=^>"<*ZK( cosu o)K {cos u) cos mk 

Durch Einfiihrung der Functionen R^, wird hieraus 

-^2 n + 1 I? (cos u') = ^ m ^* (cos u o ) l?l (cos u) cos m k 

oder ^»+iy"=V w ^ (cos u ) r*. 

Diese Gleichung ist mit der ersten Gleichung des Systems 

(4a), die auch in der Form y * = ^^ m a^ c^ geschrieben werden 

kann, identisch und liefert daher unmittelbar die in dieser auf- 
tretenden Coefficienten. Es ist danach 

( 9 ) ««■= 77=^= K ( cos O 

y2 ft -f- I 

und die Substitution dieses Resultates in die Gleichung (8) giebt 

«°> '•" = s^2"' :je:(C0,, °- 

Die Aufgabe ist hiermit im wesentlichen gelost ; nur die durch 
die Bedingung ^=0 eingefiihrte Beschrankung ist noch aufzu- 
heben. Es genugt dazu offenbar, die Entwickelung (1) in die 
Form 
V=R.^« ^ m *2 (cos u) [(gZ cos m K 

-f- h? H sin m k ) cos m (k — k p ) -f- ( — g£ sin m k 

+ h„ cos m k ff ) sin m (k — \,)] 



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VER TEIL UNG DES ERDMA GNETISCHEN PO TENTIALS 2 $ 

umzusetzen und den hierin auftretenden Factor von 
R £ (cosh) cos m (A— \ ) anstatt gZ, in ( 10) einzufiihren. Dadurch 
wird aus dieser Gleichung, wenn man noch nach Analogie der 
friiheren Abkiirzungen 

JRi (cos u ) cos m \, = C£ , RZ (cos u ) sin m \ = Sj, 
setzt, die Schlussformel 

(") J'* = 7\ — — r= y] m (^ c m + KSZ) 

\ 2 « + I ^"* 

erhalten. 



Mit Hiilfe dieser Formel, die fur n=i einen bekannten Satz 
(S. 20) ergiebt, habe ich nun die Werte von jl,jl . . . Ji und 
der daraus nach Gleichung (3) abgeleiteten Grosse F fiir 216 
Punkte N' berechnet. 1 Der Kurze halber gebe ich nur die abge- 
rundeten Werte von F, und zwar unter Weglassung des dop- 
pelten Vorzeichens und in der Einheit o f i* cm~-tg*s~\ fiir 108 
von diesen Punkten an. 



u 


X=o° 


30° 


6o° 


90° 


120° 


I5(T 


180 


210° 


240 ° 


270° 


300 


330° 


u 


0° 


50 


50 


50 


50 


50 


50 


50 


50 


50 


50 


50 


50 


180 


10° 


40 


37 


37 


49 


68 


81 


82 


73 


56 


40 


34 


38 


170 


20° 


64 


50 


24 


45 


84 


109 


in 


89 


55 


24 


29 


55 


160 


30° 


9i 


75 


37 


52 


100 


130 


126 


107 


49 


19 


41 


74 


150- 


40° 


in 


98 


59 


68 


114 


139 


124 


78 


40 


35 


54 


86 


140 


50° 


121 


115 


73 


81 


121 


137 


106 


5i 


29 


44 


59 


85 


130° 


6o° 


121 


123 


75 


81 


117 


121 


77 


20 


26 


42 


52 


7i 


120° 


70° 


109 


121 


68 


69 


102 


95 


43 


32 


35 


32 


38 


35 


110° 


8o° 


86 


109 


59 


50 


79 


63 


3i 


63 


45 


24 


34 


12 


100° 


90 


56 


90 


52 


31 


53 


26 


56 


90 


52 


3i 


53 


26 


90° 




X=i8o c 


' 210° 


240 


270' 


300 


330° 


0° 


30° 


6o° 


90* 


I20 e 


150 





Die Zahlen der mitgeteilten Tabelle, von denen sich jede auf 
zwei einander diametral gegenuber liegende Punkte, mit anderen 
Worten auf einen Durchmesser der Erde bezieht, lassen fiinf 
Minima erkennen. Keines fallt mit einem geographishen (ebenso 
keines mit einem magnetischen) Pole auch nur annahernd zu- 
sammen. Die beiden tiefsten sind etwas genauer bestimmt, 
F= 7 im Punkte A mit den Coordinaten « = 83°, \= 332 
F=i 3 " B " u = 2 5 °, X=2 77 °. 

1 Diese Berechnung lasst sich in Verbindung mit der Auswertung des Potentials 
fiir dieselben Punkte erledigen. 1st dieses, nach dem oberen Index der Kugel- 
functionen geordnet, gleich F (I >+ F (a >-f- ^ (3> + . . . .♦ so hat man offenbar im Punkte 
N\ zu dem die Functionen C*, S^ gehoren, Fc*)=^/ 2 n + ij". 



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26 A. SCHMIDT [vol. I. No, i] 

Man konnte noch die Frage aufwerfen, fur welche Punkte 
F nicht absolut, sondern relativ, namlich im Verhaltniss zu K x 
(d. i./J) kleinste Werte annimmt. Die Untersuchung dieser 
Frage fuhrt nahezu auf dieselben Punkte wie die vorhergehende 
Betrachtung ; es andert sich jedoch die Rangordnung der beiden 
in die Nahe von A und B fallenden Minima. Im ersteren wird 
(F:K X ) gleich 0,017, im letzteren gleich 0,007, wahrend sich fur 
den Pol N der Wert 0,027 ergiebt. Ein ungefahr durch B 
gehender Durchmesser ist also derjenige, fur welchen die Curve 
der Mittelwerte V n in ihrer Gestalt einer Sinuslinie am nachsten 
kommt. 

Um das Ergebnis noch deutlicher zum Ausdruck zu bringen, 
will ich diese Mittelwerte und ihre Abweichungen von der 
Sinuscurve fur die drei nach A, B und </V gehenden Durchmesser 
in derselben Weise angeben, wie es in der zu Anfang genannten 
Abhandlung (Seite 12) geschehen ist. Die dort mit "V H :R 
(berechnet) " und "Differenz" bezeichneten Columnen ent- 
sprechen den hier unter K x (cos u f ) und/i (#') stehenden. 



Pol: 


A 




B 




N 




• (") 


Kx cos u' 


A (*') 


fCt(co*v) 


A (*') 


/T(cos*) 


/(«) 


0° 


-778 


— 1 


—3M0 


14 


—3173 


106 


10° 


—766 


— 3 


—3093 


14 


—3126 


92 


20° 


—731 


— 6 


—2952 


15 


—2983 


52 


30° 


—674 


—10 


— 2720 


14 


—2749 


2 


40° 


—596 


—11 


— 2406 


10 


—2431 


—41 


50° 


— 500 


— 7 


— 2019 


4 


— 2040 


-65 


6o° 


—389 


1 


—1570 


— 4 


—1587 


-58 


70° 


—266 


9 


- IO74 


— 11 


—1085 


—27 


8o° 


—135 


13 


— 545 


—•5 


— 551 


17 


90° 





10 





—15 





—55 


100° 


135 


3 


545 


— 10 


551 


73 


110° 


266 


— 2 


1074 





IO85 


62 


120° 


389 


— 3 


1570 


12 


1587 


27 


130° 


500 





2019 


19 


2040 


— 16 


140° 


596 


2 


2406 


18 


2431 


—50 


150° 


674 


— 2 


2720 


5 


2749 


—66 


160 


711 


—14 


2952 


—15 


2983 


-63 


170 


766 


—27 


3093 


—34 


3126 


—53 


180 


778 


—32 


3140 


—41 


3173 


-48 



Die hier fiir N gefundenen, also auf die Rotationsaxe der 
Erde bezuglichen Differenzen sollten mit den von Herrn von 
Bezold a. a. O. mitgeteilten im wesentlichen iibereinstimmen. Sie 
sind indessen, ganz abgesehen davon, dass sie einen etwas 
anderen Gang besitzen, mehr als doppelt so gross wie diese. Der 



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go 3 


go" 


o,ooioo 


0,00290 


0,00284 


0,00209 


0,00163 


0,00145 


0,00368 


0,00262 



VERTE1LUNG DES ERDMAGNETISCHEN POTENTIALS 2J 

Grund dieser beim ersten Anblick iiberraschenden Verschieden- 
heit liegt darin, dass die Coefficienten^'^**^, auf denen jene Diff- 
erenzen beruhen, in dem Potentialausdrucke von Q. Icilius viel 
geringer sind, als in dem von mir benutzten (S. 21). Sie sind 
unzwefelhaft, wie ein Vergleich der Ergebnisse aller bisherigen 
Potentialberechnungen lehrt, wesentlich zu klein. Es ist namlich 

go* 

nach Gauss, 0,00230 

" Erman-Petersen, — 0,00036 

" Quintus Icilius, — 0,00164 

" Neumayer-Petersen, — 0,00234 

Dass Herr von Bezold bei seiner Untersuchung so kleine 
Differenzen fand, dass deren Realitat zweifelhaft erscheinen 
musste, lag also in dem zufalligen Umstande begriindet, dass er 
aus ausseren Gninden gerade die von Q. Icilius nach seiner 
Rechnung gezeichneten Karten benutzte. 

Aus der geographischen Verteilung der Werte des erdmagne- 
tischen Potentials kann — das ist das Ergebnis der vorstehenden 
Betrachtungen — kein Argument zu Gunsten der Annahme 
hergeleitet werden, dass der Hauptteil der erdmagnetischen 
Kraft in irgend einer Beziehung zur Rotation der Erde stehe. 
Es ist aber einleuchtend, dass dieser Satz nicht umgekehrt 
werden darf. Der Ausfall unserer kritischen Untersuchung 
beweist auch nichts gegen die Moglichkeit einer solchen Bezie- 
hung, die durch den nicht zu bezweifelnden Einfluss der Ges- 
taltung und des innern Baues der Erdrinde verdeckt sein kann. 



HALLEY'S EARLIEST EQUAL VARIATION CHART. 

[Reproduced in facsimile for the first time, from a photograph furnished by Thos, 
Ward, Esq., of the chart in his possession. Frontispiece. Text by L. A. Bauer.] 

In Nature, of May 23, 1895, the writer made known the find- 
ing of a Halley isogonic chart in the British Museum which had 
apparently escaped the attention of modern magneticians and 
bibliographers and to which Halley himself, as far as has been 
ascertained, made no reference. Upon seeing the notice, Mr. 
Thos. Ward of Northwich, England, made known in the follow- 
ing number of the same periodical the fact that he likewise pos- 
sessed a copy, bound up with other charts of the 17th and 18th 
centuries. Through his courtesy and kindness the Journal is 
enabled to present the first facsimile reproduction, as far as 
known. 1 The reduction in size is about one-fifth (0.189).* The 
facts which make this chart of great interest, as briefly stated 
as possible, are as follows: 

Edmund Halley, the noted astronomer, published at the very 
beginning of the 18th century his famous "Chart of the Lines 
of Equal Magnetic Variation " (Declination) to which renewed 
attention has just been called by Hellmann's valuable facsimile 
reproductions of the earliest magnetic charts. 3 Halley and the 
revisers of his chart, W. Mountaine and J. Dodson, invariably 
speak of one chart and generally the reference is such that it 
can be definitely settled that the chart reproduced by Airy 4 and 
by Hellmann 3 was the one had in mind. And yet Halley actu- 

x The copy in Le Monnier's Loix du Magnitisme, Paris, 1776 and 1778, is, 
according to information kindly sent by Professor Hellmann, an imperfect one; it is of 
the size 28.7 x 24.0 cm., the decorations and dedication (the matter of chief interest) 
not being given. 

»The size of the original, according to Mr. Ward is 23 x 19X in. (58.4x48.9 cm.) 
reckoned to the outside of the enclosing border, and that of the photograph which he 
furnished the Journal, 10.2x8.7 m « (25.9x22.1 cm). 

^Neudrucke von Schriften und Karten iiber Meteorologie und Erdmagnetismus. 
Herausgegeben von Professor Dr. G. Hellmann. No. 4, Berlin, 1895. A. Asher & Co. 

4 In Greenwich Observations, for 1869. 

28 



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//ALLEY'S EARL/EST EQUAL VAR/AT/ON CHART 29 

ally published two totally distinct charts, the one given here 
being unquestionably the earlier one. This matter, while of no 
practical importance, since the later chart embraced all that was 
given on the earlier one and more too, is nevertheless of histori- 
cal interest. In this light should this contribution to the history 
of terrestrial magnetism be regarded. For strange to say, although 
Halley is generally reputed as being the inventor, 5 and was 
regarded so by his contemporaries, of the fruitful method of 
representing the distribution phenomena on the earth's surface 
by drawing lines through all the places where the particular 
phenomena under question has the same numerical value, he 
nowhere apparently has written a paper on the subject. 6 He did 
not present the matter formally before the Royal Society, of 
which, as will be recalled, he was a prominent member. He 
only wrote when the accuracy of his isogonic lines was questioned. 
In consequence, much confusion has prevailed about the Halley 
chart and the mystery is not yet wholly cleared up. For con- 
venience we shall now speak of the "World Chart," meaning 
thereby the one given by Airy and by Hellmann, and of the 
"Atlantic Chart," the special subject of this sketch. 

Airy was led to reproduce the " World Chart" as he could 
find no one of his day who had ever seen a copy of Halley's 
equal variation chart. After diligent inquiry at home and 
abroad he was rejoiced to find that the British Museum possessed 
a copy, and it was thought the only copy. This chart bears the 
title "Anew and correct Sea Chart of the Whole World, shewing 
the Variations of the Compass as they are found in the year 
1700." It is very often referred to under the abbreviated Latin 
title of " Tabula Nautica." The date of its publication (the 
chart itself has no date) hitherto assigned has been 1701. 7 But 

5 According to Hellmann,3 p. 18, Christoforo Borri of Milan appears to have made 
an attempt to construct isogonics for the Atlantic and Indian Oceans in 1620. 

•The only explanation of the chart — and that is only as far as the use of it by 
seamen b concerned — is a text brought to light by Hellmann which was pasted at 
the bottom of later editions of the " World Chart." This is certainly striking when the 
importance of this piece of work is called to mind, and when it is remembered that, 
in order to construct the isogonic lines for those parts (e. g., the Indian Ocean) over 
which he had not made observations himself, a laborious search for observations and 
a reduction, possibly, to the epoch of the lines, 1700, was necessary. 

7 This date may be due to the following statement by Halley in the Philosophical 



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30 L. A. BA UER [Vol. I, No. x] 

all the copies thus far found, all of which have been personally 
examined by the writer, are dedicated by Halley as follows : "To 
His Royal Highness, Prince George of Denmark, Lord High 
Admiral of England, Generalissimo of all Her Majestie's Forces." 
Now Prince George, consort of Queen Anne, did not bear this 
title until April 17, 1702, hence the chart with the above dedica- 
tion could not have been published in 170 1, as has been supposed, 
but somewhat later, probably in 1702. It certainly appeared 
before 1705, for in that year it was given on a reduced scale, 
with the additional feature of the trade winds added, in the 
11 Miscellanea Curiosa." 8 Curiously, however, there is a reference 
in 1701 to a Halley variation chart pointed out by Hellmann, viz., 
in the Hist, de VAcad. de Paris, 1 70 1 , p. 9. Evidently, then, a chart 
prior to the one just spoken of must have been sent out by Halley. 
It is quite possible that the chart received by the Paris Academy 
in 1 70 1 was none other than the "Atlantic Chart" given here, as 
will presently appear. 

The base of the "Atlantic Chart" is entirely different from 
that of the "World Chart." It not only does not embrace the 
entire globe, but the scale of projection is slightly different, as 
also the spelling of some of the names, e. g. % "Wild Brasile" 
instead of "Wilde Brazile." Yet the equal variation or isogonic 
lines are identical with those of the "World Chart," except that 
in no case are they extended over the land, and that in a few 
instances they are slightly prolonged. It furthermore contains 
some additional features, chief of which being the laying down 
of the course of the Paramour Pink, the ship in which Halley 

Transactions, Vol. it) (unabridged), 1714, p. 165, "to examine the chart I published in 
1 70 1, for shewing at one view the Variations of the Magnetical Compass, in all those 
Seas with which the English Navigators are acquainted." 

•In the Philosophical Transactions, Vol. 23 (unabridged), 1702-3, p. 1 106, there is 
a letter by Dr. Wallis to Halley, dated Oxford, May 23, 1702, from which I extract the 
following : " I sent you a Letter about three weeks since (which, I hope you received) 
with my hearty Thanks for the Present you had then sent me ; your Map of the Mag- 
netick Variations. I look upon the thing as an excellent Design, and very Instructive, 
well Contrived, and well Executed. And which, I think was never undertaken by any, 
before you." Unfortunately no statement is made which would clinch the matter 
whether Wallis got a copy of the " World Chart " or the "Atlantic Chart." If the 
surmise that it was the former could be proven true, then would the date of publication 
of the "World Chart" be furthermore limited to the interval between April 17, and 
about May 1, 1702. 



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H ALLEY'S EARLIEST EQUAL VARIATION CHART 3 1 

made his observations between 1697 and 1701, with the help of 
which he drew the isogonic lines. The title will also be seen to 
be different. But the matter of chief interest is the dedication 
to King William III. who fitted out Halley's expedition and 
who died March 8, 1702. It is then unquestionably of an earlier 
date than the "World Chart" spoken of above. It was doubtless 
Halley's first chart and probably a preliminary one, hence 
its apparently limited circulation.* The question that remains to 
be answered is: Is the date 1701 given by Halley in the refer- 
ence quoted 7 and relating to the "World Chart," as is plain 
from the context, a slip of memory or of type, or is the copy of 
the "World Chart" with the Prince George dedication an altered 
reprint of one published in 1701, a copy of which not yet having 
been brought to light ? 

In conclusion grateful acknowledgment must be made of 
the assistance most cordially given by Mr. Coote of the British 
Museum, Professor Hellmann of Berlin and Monsieur Marcel of 
the Biblioth&que Nationale, Paris. 

9 The copy in the British Museum bears the catalogue mark of 977 (4). 



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LETTERS TO EDITOR 



ON THE BEST FORM FOR THE COMPONENTS OF SYS- 
TEMS OF DEFLECTING FORCES. 

A DISCUSSION. 
Frank H. Bigelow. 

I am constrained to offer a few remarks on the best form for the 
publication of the components of the various systems of deflecting 
forces, that disturb the normal magnetic field, which it is one of 
the first tasks of the science of terrestrial magnetism to thoroughly 
explore. The immediate impulse to this action is the recommendation 
put forth by Ad. Schmidt, Gotha, in his article " Ergebnisse der mag- 
netischen Beobachtungen zu Godthaab, 1882-3," p. 300, MeteoroL 
Zeitschrift, August, 1895. In this place he supports the proposition 
that the variations A H, A 8, of the horizontal force and declination 
respectively, be reduced to the axes X (north) and Y (east) by the 
formulae, 

A X = — p Bsin 8 . A 8 + cos 8 . A H 
A Y= p If cos 8 . A 8 + sin 8 . A H 
±Z=±Z 
I admit the correctness of this reduction and the desirability of mak- 
ing some computation for publication, to advance the signification of 
the observed absolute values of ff y D> V y towards a sound interpreta- 
tion, but I very respectfully dissent from the opinion that this change 
to the X, Y t Z axes (north, east, nadir), where X=f. cos /cos 8, 
Y=f. cos /sin 8, Z=/. sin /', is advantageous. For the discussion 
of a system in geographical latitude and longitude it may be most 
useful, as Gauss and others have found it, but for the separation of 
impressed deflecting forces from the normal field it is not conducive 
to simple results with minimum expenditure of work. This conclu- 
sion depends upon some distinct reasons : 

1. The formulae for A X, A K, contain each two terms, and although 
it may not be an important consideration to do the work at a single 
station in this way, it really becomes a serious barrier, if not an 
obstacle, to undertake any computation covering many stations and 
comprising several years of observations. The simplest possible form 

33 



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LETTERS TO EDITOR 33 

of work will alone survive the test of actual operation. The fact that 
two terms instead of one is suggested is of itself a weighty argument 
against accepting it generally. 

2. It is recognized that the computation of the vector forces that 
are impressed upon the individual stations, at any given time, is the 
high road to advancement in the interpretation of magnetic observa- 
tions. Now a vector to be really intelligible must present itself to the 
mind, not in the form of rectangular components, A X, A K, A Z, but 
in its spacial relations, having a definite direction (azimuth, altitude) 
and length at the place of observation. Obviously, polar coordinates, 
equivalent to the rectangular, are alone capable of giving this effect. 
In my own work, the altitude angle a, the azimuth angle /?, and the 
vector length s, derived from the observed variations A If, A D, A V, 
have always been used with satisfaction and success. The form of 
computation is as follows : &H, AZ>, A V \ dx, dy, dz | <r, s, a, fi | , 
where A H, A D, A V, are the observed variations in scale divisions, or 
in any system of units ; dx, dy, dz, the equivalent values in c . g . s. 
units ; 

<r = - j dx t + dy\ s = Jdx* + dy 9 + dz\ tan a = — , tan p = Q 
\ \ <r dx 

the rotation being anticlockwise instead of clockwise, as Schmidt pro- 
poses. The reason for this is that westerly declination is positive, and 
the anticlockwise rotation follows the usual trigonometric movement. 
I have never taken the trouble to compute by these square-root for- 
mulae, but have used a diagram scale, which does well enough for 
practical work in a large field of operations (see Weather Bureau 
Bulletin, No. 2, 1892, "Notes on a New Method for the Discussion of 
Magnetic Observations "). In that paper a complete example of work 
is given. Two simple entries on the diagram, first, dx, dy, and then 
<r, dz, are sufficient to give us s, a, /?. 

3. It must be shown, before adoption, that the axes X, Y, Z, have 
some very significant advantage over H, D, V, for the elucidation of 
magnetic impulses. The secular wandering of the magnetic meridians 
over the earth's surface would, at first sight, seem an argument in favor 
of adopting fixed geographical axes, but this is offset by the fact that 
magnetic impulses are instantaneous, and are not to be reduced to any 
epoch by secular corrections. Furthermore, the impulses ought to be 
referred to their extra-terrestrial axes of approach, freed from astrc- 
nomical relations. Also the distortion of the cosrnical lines of force as 
they enter the earth are so conspicuously functions of the permeable 
material of the earth, regarded as a magnetic shell, that the' station 



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34 A. SCHMIDT [Vol. I. No. i] 

values are really alone of practical importance. At any rate the sub- 
ject must have made marked advances before it will pay to adopt any 
other system of axes, either geographical or extra-terrestrial in place" of 
the magnetic station lines of reference to H y D, V. 

Our knowledge of the lines of approach to stations is now sufficient 
to show that it is not the geographical pole, nor the magnetic pole 
alone, but a combination of the two, which is the effective polar seat of 
equivalent disturbance variation. The aurora belt marks out definitely 
the places of entry of the external field, showing concentration of 
forces in the rough ovals embracing the two poles, the center of opera- 
tions lying say mid-way between them, and yet not so in a strictly 
physical sense. (See Amer. Journ. Sci., August 1895, p. 88). 

My conclusion is that station rectangular variations A H % A D, A V 9 
should be transformed into station polar coordinates of the equivalent 
vector s t a, /?, as the simplest to work, and the most instructive when 
done. It seems proper in this place to propose the following modifica- 
tion of, or rather addition to, the form of publication adopted by the 
International Polar Commission. Having given in c. g. s. units the 
observed absolute values of H, Z>, V, let a page more be devoted to a 
display of the two sets of <r, s t a t f3: 

I. Those equivalent to the variations of the mean daily values on the 
monthly mean. 

II. Those equivalent to the variations of the mean hourly values on the 
monthly mean. 

The former are obtained by subtracting the monthly mean along 
the right-hand column, and the latter by subtracting the monthly mean 
along the lowest row on the page as usually printed, for A H f A D, A V y 
whence the transformation to <r, s, a, P proceeds. 

The interest of terrestrial magnetism as a science depends largely 
upon the construction of these station vectors, whence wide physical 
laws can be deduced. The labor of such transformation should be 
shared by the several stations, exhibiting their work in a form advan- 
tageous to physicists generally. 

Washington, D. C m October 28, 1895. 

Adolf Schmidt. 

Der Herr Redakteur hat die Freundlichkeit gehabt, mir Einblick 
in das von Herrn Professor Bigelow an ihn gerichtete Schreiben zu 
gewahren, und ich benutze gem die Gelegenheit, ihm meine Ansicht 
uber die von Herrn Bigelow darin beruhrte Frage auseinanderzusetzen. 

Bigelow ist mit mir in dem Wunsche einverstanden, dass die 



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LETTERS TO EDITOR 35 

Observatorien ihre Beobachtungen in einer Form verdffentlichen moch- 
ten, die eine moglichst directe und bequeme Verwendung bei 
theoretischen Untersuchungen gestattet ; er weicht von mir in dem 
Urteile dariiber ab, welches die beste, d. h. fiir die meisten Zwecke 
taugliche Form der Darstellung sei. In seinen ErSrterungen fliessen 
dabei zwei Momente zusamraen, die ich, da sie von einander voll- 
kommen unabhangig sind, hier getrennt betrachten mochte. Er giebt 
erstens den polaren Coordinaten des Kraftvectors den Vorzug vor 
seinen rechtwinkligen Componenten ; zweitens will er das Coordinaten - 
system nicht nach dem astronomischen, sondern nach dem magne- 
tischen Meridiane orientiert wissen. 

Ich werde mit dem zweiten Punkte beginnen, in dem ich 
Bigelow entschieden entgegentreten muss, wenn es mir auch fast 
scheint, als ob er selbst kein sehr grosses Gewicht darauf legt. Die 
Beziehung auf den astronomischen Meridian hat den wesentlichen 
Vorteil zur Folge, dass an jedem einzeinen Orte ein festes, nicht mit 
der Zeit veranderliches Coordinatensystem gewonnen wird, und dass 
die zu verschiedenen Orten gehorigen Systeme in einfacher Lagen- 
beziehung zu einander stehen. Dies ist natiirlich fiir jede zusammen- 
fassende Untersuchung, die die Erscheinungen nicht ausschliesslich 
als lokale Phanomene betrachtet, von der grossten Bedeutung. (Fiir 
einzelne Zwecke wird es sich vielleicht einmal nutzlich erweisen, noch 
weiter zugehen und die Axen an alien Punkten denjenigen eines 
bestimmten, sei es im Raume festen, sei es mit der rotierenden Erde 
verbundenen Coordinatensystems parallel zu wahlen.) Einzelunter- 
suchungen andrerseits, die sich nicht auf verschiedene Orte oder Zeit- 
punkte beziehen, werden durch die Wahl eines festen, astronomisch 
orientierten Systems in keiner Weise erschwert. Diese Wahl erfolgt 
somit allein aus dem formalen Gesichtspunkte, dass sie theoretisch 
betrachtet die einfachste und ubersichtlichste, fiir die Betrachtung der 
Erde im Ganzen sogar fast die einzige brauchbare ist. Vor allem ist 
zu betonen, dass dieser Wahl keinerlei Hypothesen iiber die Natur der 
die Variationen hervorrufenden Krafte zugrunde liegen, wie Bigelow 
zu meinen scheint, wenn er u. a. sagt : "The impulses ought to be 
referred to their extra-terrestrial axes, freed from astronomical rela- 
tions." Ira Gegenteil beruht gerade die Beziehung auf den magne- 
tischen Meridian auf durchaus unnotigen und, wie ich meine, auch 
unwahrscheinlichen Voraussetzungen. Gerade diese Beziehung zu wah- 
len, bei der iraraer noch die Declination gegeben sein muss, wenn eine 
bestimmte Angabe gemacht werden soil, hat doch nur dann einen Sinn, 
wenn man dadurch eine einfachere Gesetzmassigkeit der Erscheinungen 



36 A. SCHMIDT [vol. I. No. i] 

zu finden hofft. Nun liegt bis jetzt kein Grand zu der Annahme vor, 
dass die verschiedenen Variationen der erdraagnetischen Kraft in ein- 
facher Weise von der lokalen Mittelrichtung dieser Kraft abhangen, 
insbesondere, dass sie auch mit dieser zugleich genau entsprechenden 
saecularen Aenderungen unterliegen. Es ist auch kaum einzusehen, wie 
eine derartige Beziehung physikalisch m6glich sein sollte. Will man 
also ohne vorgefasste Meinung an das Studium der Erscheinungen 
herantreten, so ist es sicherlich am besten, diese zunachst in einem 
festen, nur nach formalen (mathematischen) Rucksichten gewahlten 
Coordinatensysteme zu registrieren und abzuwarten, ob etwa die 
Erfahrung zeigen wird, dass fur das eine oder andere Phanomen eine 
seiner Natur besser angepasste, specielle Form der Darstellung 
existiert. 

Nicht recht verstandlich ist mir die Bemerkung, dass die magne- 
tischen Impulse instantan seien und daher keine Correctionen zur 
Reduction auf eine bestimmte Epochebedurfen, da es sich ja nicht um 
eine Veranderung des Vectors, sondern nur um eine zur Erzielung 
einer genauen Vergleichbarkeit erforderliche Abanderung der Form 
seiner Darstellung handelt. 

Zum Schlusse sei noch darauf hingewiesen, dass, wenn man einma 
die Coordinaten auf den magnetischen Meridian beziehen will, dann 
auch consequenter Weise als Hauptaxe nicht die Verticale, sondern die 
Richtung der Inclinationsnadel gewahlt werden miisste. Man kame 
damit auf die fur viele Zwecke gewiss nutzliche Form, die Liznar 
besonders zu graphischen Darstellungen empfohlen hat, (vergl. 
Wiener Sitzungsberichte C, Abt. II., Nov. 1891, pag. 1153), und die 
Bauer bei der Untersuchung der Saecularvariation angewendet hat. 

Anders verhalte ich mich gegenuber der Frage, ob rechtwinklige 
oder Polarcoordinaten anzuwenden seien. Ich meine, dass je nach der 
Natur der Aufgabe bald diese, bald jene zweckmassiger sein konnen. 
Deshaib wiirde ich es fur sehr niitzlich halten, wenn in den Jahrbiichern 
der Observatorien beide Darstellungen (nur mit dem wahren Azimut 
P-\- D an Stelle von /J, also mit den Werten s, a, /J-f D) angegeben 
wurden. Will man sich aber auf eine Darstellung beschranken, so 
halte ich allerdings diejenige durch die rechtwinkligen Componenten 
&X> A Y t AZ fur die weitaus wichtigere, weil allgemeiner verwendbare. 
Der einzige von Bigelow dagegen angefuhrte sachliche Grand kommt 
auf die Behauptung hinaus, dass die Darstellung durch Gesamt- 
intensitat und Richtungswinkel anschaulicher sei, als diejenige durch 
Componenten. Seibst wenn dies richtig ware (was ich bezweifle, da 
dabei sicherlich die Gewohnung von grossem Einflusse ist), so wurden 



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LETTERS TO EDITOR 37 

doch die letzteren vorzuziehen sein, weil sich mit ihnen bequemcr 
rechnen und analytisch operieren lasst. Fur die Gewinnung einer rich- 
tigen und umfassenden Anschauung werden doch stets graphische 
Darstellungen ein unersetzliches Hulfsmittel bleiben ; von der zahlen- 
massigen Darstellung ist in erster Linie zu fordern, dass sie moglichst 
den Bediirfnissen der Rechnung angepasst sei. Das ist aber nur bei 
der Angabe der Componenten der Fall. Nur diese gestatten eine ein- 
fache Zusamraensetzung und Zerlegung in mehrere Bestandteile, die 
Bildung von Mitteln u. dgl. Wie umstandlich sind nicht alle diese 
Operationen bei der Benutzung von Polarcoordinaten. Und doch sind 
sie fortwahrend ndtig, zumal da unzweifelhaft die thatsachlichen 
Variationen der erdmagnetischen Kraft aus dem Zusamnienwirken 
einer ganzen Reihe von Einfliissen entspringen. Und wenn man nicht 
die Vorgange an einer einzelnen Station, sondern die Erscheinungen 
auf der ganzen Erde zusammenfassend oder vergleichend betrachtet, 
so tritt die durch die Benutzung der Componenten erzielte Verein- 
fachung noch deutlicher hervor. 

Den Hauptvorteil der Verwendung von Polarcoordinaten (die 
zugleich mit ihm auch Liznar, Wiener Sitzungsberichte CI, Abt. II., 
Febr. 1892, pag. 87, eingefiihrt hat) sieht indessen Bigelow in der 
geringeren Arbeitsleistung, die zu ihrer Berechnung notig sei. Mit 
der starken Betonung dieses Arguments kann ich mich nicht einver- 
standen erklaren. Wenn irgend eine Arbeit fiir den Fortschritt der 
Wissenschaft unerlasslich ist, so muss sie eben geleistet werden, und 
sie wird es auch fniher oder spater; die Bemerkung: "The simplest 
possible form of work will alone survive the test of actual operation " 
gilt nur insoweit, als durch die vereinfachte Behandlungsweise die 
Brauchbarkeit der Ergebnisse nicht verringert wird. Nun ist aber 
obendrein die mit der Berechnung der Componenten verknupfte 
Arbeit keineswegs sehr betrachtlich. Zunachst handelt es sich ja hier 
nur um die Forderung, jedes Observatorium solle alljahrlich etwa die 
Monatsmittel des taglichen Ganges von A' und Kableiten, was genau 
dieselbe, den sonstigen Reductionsrechnungen gegenuber verschwin- 
dende Arbeit erfordert, wie die vielfach iibliche Ableitung des Gan- 
ges der Totalintensitat und der Inclination. Dann aber ist mir 
die Meinung Bigelow's, dass die Ermittelung der Componenten 
AiV,Ay,AZ, miihsamer sei, als die Bestimmung der polaren Bestim- 
mungsstiicke s, a, /?, vollkommen unbegreiflich ; es ist eher das Gegen- 
teil der Fall. Fast scheint es, als meine er, bei der Bestimmung der 
letzteren konne man sich graphischer Methoden bedienen, zur Her- 
leitung der ersteren aber musse man durchaus den Weg der Rechnung 



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38 A. SCHMIDT [Vol. I, No. r] 

benutzen. Ein Unterschied besteht allerdings in dieser Beziehung. 

Die Forrneln zur Berechnung von s, a, ft sind so unbequem, dass die 

Benutzung eines Diagramms die Arbeit ausserordentlich vereinfacht ; 

dagegen ist bei A X und A Y mit Benutzung von Multiplicationstafeln 

oder ahnlichen Hiilfsmitteln die (dann leicht ganz im Kopfe auszufuh- 

rende) Rechnung bei grosserer Scharfe kaum umstandlicher als die 

graphische Ermittelung. Was nun den fiir die letztere notigen 

Arbeitsaufwand betrifft, so gestaltet er sich in den beiden Fallen fol. 

gendermassen. Es ist offenbar (mit Bigelow's Bezeichnung) 

A X= — dy sin D + dx cos D t A F— dy cos Z> + dx sin D. 

Die Berechnung von A X, Ay, &Z(=dz) kann also nach dem Schema 

A^,AZ>,AF | dx,dy,dz \ <r,a,p+D | AJf,AK,AZ 

erfolgen, indem 

dy 

erst <r = Jdx° + dy a , tyP = -j L , und dann A X = <r cos (fi + &), 

A Y= <r sin (p + H) 

durch je einmalige Benutzung des Bigelow'schen Diagramms gefunden 
wird. Offenbar erfordert dies genau dieselbe Arbeit, wie die Ablei- 
leitung von s, a, ^. (Scheinbar ist eine, freilich minimale Mehrarbei t 
in der Bildung der Summej8+Z?zu leisten ; aber diese hat, abge- 
sehen davon, dass sie durch eine veranderte Bezifferung des Diagramms 
eliminiert werden konnte, nichts mit dem Gegensatze von recht- 
winkligen und Polarcoordinaten zu thun, sondern beruht auf der 
Verschiedenheit der Azimutzahlung.) Nun kann man aber offenbar 
die Ermittelung von AI,AK noch vereinfachen und auf die einmalige 
Benutzung eines Diagramms, das aus zwei um den festen Winkel D 
gegeneinandergedrehten, rechtwinkiigen Netzen besteht, beschranken. 
Wie man diese am zweckmassigsten einrichtet, bedarf wohl keiner 
Erlauterung. Ebenso braucht wohl kaum darauf hingewiesen zu 
werden, dass man die Bestimmung von dy (und notigenfalls dx) 
ersparen kann, wenn man das eine Netz fiir jeden Fall besonders 
construiert. Man wird dies natiirlich nur thun, wenn die zu erzielende 
Ersparnis die Miihe der Construction lohnt. 

Zeigt sich so, dass man A X, A K, A Z sogar noch schneller, als s, a, ft 
finden kann, so 'sieht man andrerseits leicht ein, dass sich die Bestim- 
mung beider Systeme von Grossen bequem und mit einigem Vorteil 
verbinden lasst. Ich schliesse mich deshalb der von Bigeiow an die 
Vorstande der Observatorien gerichteten Aufforderung mit der 
Abanderung an, dass ich wiinsche, 

es mochten unter alien Utnstanden die Variationen der Componenten^ 
A^T,AK,AZ 



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LETTERS TO EDITOR 39 

und, wenn irgend ntbglich, auch die Werte von s, a, /? + D (nicht 
von fi>) abgeleitet und publiciert werden. 

Es ware sehr erfreulich, wenn auch von andrer Seite Stellung zu der 
vorliegenden Frage genommen wiirde, was nur dazu dienen konnte, 
die Erfullung der ausgesprochenen Wiinsche zu beschleunigen.' 
Sollte dies der Fall sein, so wiirde sich Herr Bigelow durch die von 
ihm gegebene Anregung unzweifelhaft ein grosses Verdienst um die 
Sache der theoretischen Erforschung des Erd magnetism us erworben 
baben. 

Ich kann nicht schliessen, ohne wenigstens einige Worte iiber die 
von Bigelow im Voriibergehen beriihrte Frage der Festsetzung der 
Vorzeichen zu sagen. Es ist durchaus meine Meinung, dass man sich 
darin dem heutzutage in der theoretischen Physik wohl allgemein 
ublichen Gebrauche anschliessen, d. h. positiv gegen die Bewegung des 
Uhrzeigers zahlen solle. Dadurch wird aber der positive Drehungssinn 
in der Erdoberflache keineswegs bestimmt, sondern er wird nur in 
eindeutige Beziehung zur Richtung der positiven Normalen gesetzt. 
Lasst man diese nach Innen gehen, so muss man westliche Werte von 
D und Y negativ rechnen ; will man letztere umgekehrt positiv 
nennen, so muss man sich entschliessen, nach unten gerichtete Ver- 
ticalkrafte und nordliche Inclinationen als negativ zu bezeichnen. Da 
man dies doch wohl kaum zweckmassig finden wird, und da es andrer- 
seits gewiss besser ist, die magnetische Declination in demselben Sinne 
wie das geodatische Azimut zu zahlen, als umgekehrt, so scheint mir 
auch jetzt noch die erste der beiden angegebenen Moglichkeiten den 
Vorzug zu verdienen. 

Goth a, den 20. November 1895. 



OLD MAGNETIC DECLINATIONS. 

On account of the renewed interest being paid to old magnetic 
observations, I should like to inform you that I am continuing my 
researches, the results of which I published in my paper, " De Isogonen 
in de XVI** en XVII** Eeuw, Utrecht, 1893." 

The large number of old ship journals, in the government archives 
at The Hague, furnished me with a thousand new declinations, which 
enabled me to drawisogonic maps for the period 1 540-1680, given in 
the above publication. From journals of later date, particularly for 

z It is to be hoped that this wish of Dr. Schmidt's will be fulfilled and that the 
matter brought forward in the above letters will receive the attention its importance 
merits with the result that others will be induced to take part in the discussion. — Ed. 



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40 IV. DOBERCK [Vol. I. No. ij 

the years 1630-1720 and of the travels from Holland to the Cape of 
Good Hope, also found in the government archives, I have made 
extracts. There are, besides still older journals there, which were not 
used in the maps referred to. Among others, the independent 
observations made on four ships that sailed in company from India to 
Holland in the year 1677, are very valuable. 

The journal of the famous Antonio van Diemen, and that of a ship, 
" De Noord-Beveland," contain observations in the neighborhood of 
the islands of Amsterdam and St. Paul, viz., 1633, June 17, 38 20' 
S, 77 30' E, 25 o' West Declination; 1757, Amsterdam, SSE^S, 
8-9 geogr. miles, 17 o' West Declination. 

In the " rotario" of Hessel Gerritz (1627-8), mention is made of 
an important observation in 1624 by the pilot Jan Carstensz, whose 
vessel lay anchored off the south side of the island of Granada in lati- 
tude 12 9' N, on the shore of which he observed 4 easterly declina- 
tion. 

Most remarkable also are the observations made on one of the 
ships with which the admiral Hendrik Brouwer visited Chili in the 
year 1643. Supposing an easterly current of twenty miles daily, their 
observations to the west of Chili are : 

1643 May 4 49 30 'S, 94 E. o° 25' E. DecPn. 

" 8 44 89 10 " 

41 13 43 50 81 36 " 

" 24 42 40 73* 5 25 " 

Though it is possible that the compass used had an index error, 
still these observations seem to make certain the existence of an agonic 
oval in the Pacific; they are in fair accordance with the isogonics 
drawn in my map for the year 1640. 

Although this work progresses slowly, I hope to be able to publish 
soon an improved series of isogonic maps for the 16th and 17th cen- 
turies and the first part of the 18th. 

W. van Bemmelen. 

Leyden, October 19, 1895 



SOME OBSERVATIONS OF MAGNETIC INCLINATION 

IN CHINA. 

While engaged on a meteorological mission in China in 1883, I 
made some observations of the magnetic dip. The observations in 
Hong Kong were made in the public gardens, as the observatory was 
not yet built. The observation in Swatow on the 10th of October was 
made at the British Consulate ; on the 3d of November, at the English 



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EDITORIAL GREETING 



41 



Presbyterian Mission's Compound. The observations in Amoy were 
made in the garden attached to the residence of the Commissioner of 
Customs. In Takow, they were made at the Custom House, and at 
South Cape, Formosa, in a sheltered spot near the lighthouse. 



Place 


Date 1883 






Local Mean Time 


Dip (North) 


*Lat. N. 


•Long 
£. of Gr. 


liong Kong, 


November 5 


- 


- 


5 h 


2 ro 


p.m. 


32° 


17' 


22° 17' 


II4 IO 


« 


9 


- 


- 


5 





" 


32 


19 






Swatow, 


October 10 


- 


- 


5 


26 


" 


34 


23 


23 21 


Il6 40 


** 


November 3 


- 


- 


11 


3o 


a.m. 


34 


17 






Amoy 


October 14 


- 


- 


3 


50 


p.m. 


36 


45 


24 27 


Il8 04 


•* 


16 


- 


- 


5 


10 


tt 


36 


50 






Takow 


24 


- 


- 


3 





«« 


32 


54 


22 36 


120 16 


South Cape 


27 


- 


- 


4 





i« 


31 


24 


21 55 


120 51 


«< 


28 


- 


- 


4 


30 


" 


31 


27 h 






u 


29 


- 


- 


3 


20 


a 


3i 


244 
























W. DOBERCK. 


Hong Kong Observatory, October 8, 


, 1895. 











EDITORIAL GREETING. 

With this issue appears the first number of a journal devoted exclu- 
sively to Terrestrial Magnetism, and its allied subjects such as Earth 
Currents, Auroras, Atmospheric Electricity, etc. No apology will be 
made for thus adding one more to the already over large list of scien- 
tific periodicals. Indeed, it is this very multiplicity, making it possible 
for articles on Terrestrial Magnetism to appear anywhere but specially 
nowhere, that has made the need of concentration keenly apparent to 
the lovers of the science. 

Primarily, the aim of this Journal will be, to create a broader sym- 
pathy and to afford an easier communication between widely separated 
workers in a field that is day by day receiving greater recognition and 
whose possibilities have not yet been fathomed ; secondarily, to increase 
the army of workers and of students. 

Without doubt one of the chief wants of Terrestrial Magnetism 
today is a convenient channel for the timely and friendly interchange 
of ideas among the specialists in the science. There is not a single 
journal, at present, that supplies this want. The literature is in conse- 
quence scattered over many and miscellaneous periodicals, often well- 
nigh buried away in obscure publications or in such as are only 

* These two columns were kindly supplied by Mr. G. W. Littlehales, Chief of 
Division of Chart Construction, U. S. Hydrographic Office, from the descriptions given 
in above letter. — Ed. 



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42 EDITORIAL GREETING [vol. I, No. i] 

accessible to a select few. In how far the Journal will fulfill its prime 
purpose will depend principally upon the co-workers in the science. 
Now that Terrestrial Magnetism has an organ of its own — and that an 
international one — it behooves them to do their utmost to make the 
Journal in every sense a success and thus to justify the important step 
Terrestrial Magnetism has taken. 

It is also the firm belief that the Journal should make it a special 
object to increase the ranks of the devotees by enlisting the interests 
of all the men of science who can contribute, whether directly or 
indirectly, towards the advance of the subject, such as astronomers, 
geographers, geologists, meteorologists, particularly, however, phys- 
icists and mathematicians. Here is a field full of interesting and 
fascinating problems, both of an experimental and of a theoretical 
nature, which can form the basis of legitimate and fruitful investiga- 
tions. It is the intention, therefore, to have recognized authorities 
review the progress made in the various phases of the subject and 
to point out the direction in which further research is desirable and 
essential. 

The day has gone by for studying the phenomena of the magnetized 
needle chiefly by reason of their possible value to the mariner and the 
surveyor. The higher view, ushered in by Humboldt and Hansteen, 
but most fully recognized by Gauss, that Terrestrial Magnetism is a 
subject worthy of the profoundest physical and mathematical study, 
has taken firm root and is steadily, though slowly, making progress. 
It gave birth to the famous Magnetic Union headed by Gauss and 
Weber. The epoch-making results which were the direct and indi- 
rect outcome of this magnetic association were equally beneficial to 
Terrestrial Magnetism and to science in general. It taught the physi- 
cist, among other things, how to make absolute magnetic measure- 
ments, and soon revealed to the scientific world that the Earth's mag- 
netism is in sympathetic touch not alone with terrestrial but also with 
cosmic a I influences. Hence, gravitation is not the only bond that binds 
us in friendly union with our sister planets and our parent Sun. The 
magnetic needle thus has become a most promising instrument of 
research, not alone in terrestrial but also in cosmical physics. No 
other mechanical means is so surely and so completely recording the physical 
history of terrestrial and cosmical changes as the self-registering magneto- 
graphs of our magnetic observatories, whereby the fitful tremors of the 
delicately suspended magnetic needle are being indelibly fixed on the sensi- 
tized sheet. " On that paper ; as Maxwell eloquently expressed it, the never 
resting heart of the earth is now tracing in telegraphic symbols, which will 



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EDITORIAL GREETING 43 

one day be interpreted, a record of its pulsations and its flutteritigs, as 
well as of that slow but mighty working [the secular variation] which 
warns us that we must not suppose that the inner history of our planet is 
ended." This extract suffices to give a hint as to the possibilities of 
geomagnetic investigations. In directing our eyes and energies sky- 
ward to unravel the phenomena of the starry firmament, let us not 
forget that the Earth, too, has its secrets and its mysteries that ought 
to be disclosed. Is it not geophysical observatories, generously equipped 
and endowed, that we especially need today? 

In conclusion grateful acknowledgment must be made to the Asso- 
ciates and to all those who have in any way lent their cooperation in 
the establishment of the Journal. Special mention should be made of 
Prof. Eschenhagen, of Potsdam, and Dr. Schmidt, of Gotha, for their 
warm interest and their valuable suggestions. The Journal is to be 
congratulated in that it enjoys the kindly and active interest of Prof. 
Michelson, and is to be published under the auspices of the Ryerson 
Physical. Laboratory. It is also gratifying to state that the editorial 
assistance of Dr. Mendenhall has been secured. To him will be 
referred all matters relating to Atmospheric and Telluric Currents. 
Prof. P. Wernicke, mathematician and linguist, has kindly promised 
his assistance in the handling of foreign matter. In the bibliograph- 
ical department, the valuable assistance of Mr. Oliver L. Fassig, 
Librarian of the Weather Bureau, U. S. A., has been obtained. 

That this Journal is a timely one is amply shown by the full list on 
the next page of the Associates on the editorial staff. It will be seen 
that there is a truly international representation of foremost investiga- 
tors. The size of the Journal was originally to have been about 32 
pages. With such favor, however, was the idea of such a publication 
generally received that it became at once necessary to decide upon an 
enlargement in order that the purposes of the Journal might be 
adequately fulfilled. 




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LIST OF ASSOCIATES 



Abbe, Cleveland, 1-rof., United States Weather Bureau, Washington, D. C. 
Baracchi, Pietro, Acting Gov't Ast'r to the Colony of Victoria, Melbourne. 
Bezold, Wilhelm von, Geheimrat, Dir., K. Preuss. Meteorol. Institut, Berlin. 
Biese, Ernst, Director, Meteorological Observatory, Helsingfors, Finland. 
Bigelow, Frank H„ Prof., United States Weather Bureau, Washington, D. C. 
Borgen, C, Prof., Vorstand, K. Marine-Observatoriums, Wilhelmshaven. 
Chistoni, Ciro, Professor di Fisica nella R. University di Modena, Italy. 
Doberck, William, Director of Hong-Kong Observatory, China. 
Eschenhagen, Max, Prof., K. Preuss. Meteorol.- Mag. Obs., Potsdam. 
Hann, Julius, Hofrat, Dir., K. K. Central-Anstalt fUr Met. u. Erdraag., Vienna, 
Hellmann, Gustav, Prof., Vice-Director, K. Preuss. Meteorol. Inst., Berlin. 
Hepites, Stefan C, Director, Roumanian Meteorol. Institut, Bucharest. 
Goldhammer, Dimitry A., Professor, University of Kasan, Russia. 
Lancaster, A., M£teorologiste-Inspecteur, Royal Obs., Uccle, Belgium. 
Lagrange, C, Magnetic Observer, Royal Observatory, Uccle, Belgium. 
LemstrOm, Selim, Professor of Physics, University of Helsingfors, Finland. 
Littlehales, G. W„ Chief, Div. Chart Constr., U. S. Hydrographic Office. 
Liznar, Joseph, Dr., K. K. Central- A nsalt fur Meteorol. u. Erdmag, Vienna, 
Mendenhall, Thomas C, President Worcester Polytechnic Institute, Mass. 
Moureaux, Th., Chef du Service magnlt. a V Obs. du Pare St.-Maur, pres Paris. 
Nipher, Francis E., Prof, of Physics, Washington University, St. Louis, Mo. 
Palazzo, Luigi, Prof., R. Ufficio Centrale di Meteorologia, Rome, Italy. 
Rijckevorsel, van, Dr., Conducting Magnetic Survey of the Netherlands. 
Rucker, Arthur W„ F.R.S., Prof, of Physics, Royal Coll. of Sci., London. 
Schering, Ernst, Geheimrat, Dir. Gauss Magnetic Observatory, Gtittingen. 
Schmidt, Adolf, Doctor, Gymnasiallehrer, Gotha, Germany. 
Schott, Charles A., Assist, U. S. Coast and Geod. Survey, Washington, D. C. 
Schuster, Arthur, F.R.S., Professor of Physics, Owens College, Manchester. 
Snellen, Mauritz, Chief Dir., R. Meteorol. Inst, of Netherlands, Utrecht. 
Solander, E., Lektor, Wenersborg, Sweden. 

Stok, I. P. van der, Director of Meteorol. -Mag. Obs., Batavia, Java. 
Stupart, R. F., Dir., Mag. Obs., Toronto and of Meteorol. Service of Canada. 
Tillo, Alexis de, Genlral de Division, Excellence, St. Petersburg, Russia. 
Wild, Heinrich, Professor, Zurich, Switzerland. 



44 



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NOTES 

Personals. Prof. H. Wild, having resigned his directorship of the 
Physikalisches Central Observatorium of St. Petersburg, has returned to his 
native country and has taken up his residence in Zurich. — Dr. M. Eschen- 
hagen, in charge of the Royal Magnetic Observatory at Potsdam, and Dr. 
Luigi Palazzo, of the Ufficio Centrale di Meteorologia e di Geodinamica, 
Rome, have been made professors. — Prof. J. Hann is lecturing this semes- 
ter at the Imperial University of Vienna on the results of geomagnetic 
investigations. — Dr. B. Weinstein, who includes among his lectures at the 
Berlin University, a series on terrestrial magnetism, has been elected to an 
extraordinary professorship in physics. — Mr. R. L. J. Ellery, formerly in 
charge of the Melbourne Observatory, has been retired and is succeeded by 
his chief assistant, Mr. P. Baracchi. — Prof. F. E. Nipher, to whose pri- 
vate enterprise is due the only detailed magnetic state survey in this country, 
has recently published a mathematical treatise on electricity and magnetism 
for advanced undergraduate students (J. L. Boland, St. Louis, Missouri). 

According to information received from Dr. van Rijckevorsel, he and Dr. 
van Bemmelen have been engaged during the past summer in making the 
preliminary arrangements for the investigation of the influence of elevation 
above sea level on the magnetic elements. After a careful consideration it 
was concluded that the best, and possibly the only, mountain in Europe, ful- 
filling the requisite conditions for their purpose, would be the Rigi. The 
object of this summer's work was to ascertain whether the Rigi itself exerts 
a disturbing influence upon the magnetic needle. The necessary observations 
have been made, but the computation is not yet completed. 

The necessity of a Magnetic Observatory at Melbourne. — The editor is in 
receipt of a letter from Professor Schuster calling attention to the desira- 
bility and absolute necessity of the re-establishment of the Melbourne Mag- 
netic Observatory, not only on account of the extreme paucity of magnetic 
observatories in the southern hemisphere, but especially on account of the 
extreme southerly magnetic latitude of Melbourne. He says : " I hope that 
in an early issue of the Journal you will draw attention to such places of our 
globe where magnetic observatories are most needed, and where they could 
be maintained without much trouble. I understand, for instance, that little is 
known about the present magnetic constants in Australia. There are several 
very competent physicists in Australia who I am sure would help in the mat- 
ter, did they realize its importance. In many cases I am sure they believe 

45 



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46 NOTES [Vol. I, No. i] 

that we know as much as we need." With regard to the work done at 
Melbourne since Neumayer's time the following extract from Mr. BaracchTs 
letter will inform us. " Although I have been in charge of the magnetical 
work here for the last three years, I could never (owing to my astronomical 
occupations) give it any more time than was necessary for the absolute meas- 
urements (nine or ten times a year) and for keeping the required control over 
the self-registering instruments. And I regret having to say that the daily 
curves of declination, horizontal and vertical force, have not been systemati- 
cally measured since Professor Neumayer worked out his results for the epoch 
1858-62, so that hardly any systematic use has been made of the records, 
which extend without serious interruption over thirty years. " 

How Terrestrial Magnetism has been represented at some of 
the National Assemblies during the year 1895. 
Siebente allgemeine Versammlung der Deutschen Meteorologischen Gesell- 
schaft su Bremen, April, i8qj. — This meeting was held in connection with 
the "XI. Tagung des deutschen Geographentages." At the latter inter alia 
the question of antarctic exploration was discussed by Messrs. Neumayer, van 
Drygalskiand Vanhoffen and a paper was presented by Wagner of GSttingen, 
on the development of the compass charts. At the former the following papers 
on terrestrial magnetism were presented. IV. von Bezold: " Ueber die Isano- 
malen des erdmagnetischen Potentials.*' Von Bezold's " isanomalous lines of the 
geomagnetic potential " are those lines drawn on the earth's surface connect- 
ing the places having the same departure (with due regard to sign) from the 
normal potential which is taken as equal to the mean value of the potential 
along the parallel of latitude passing through the particular place. He fully 
developed the theory of these lines and reached some interesting conclusions. 
The paper was presented in outline for the first time before the Berlin Acad- 
emy on January 19, 1893, and in its entirety on April 4, 1895, and has now 
been printed in full.' G. Hellmann: " Magnetische Karten des 18. Jahr- 
hunderts." Very slowly, said the speaker, did the knowledge that the magnetic 
needle does not point truly north gain headway. The earliest mention of the 
fact in a printed work occurs in 1527, and in 1532 it is graphically pictured 
for the first time. After giving a brief account of his reproduction of the earliest 
magnetic charts, he exhibited eleven original charts of the 1 8th century in 
his possession. For three centuries, he said, the study of terrestrial mag- 
netism has been mainly kept alive by the service it renders to the mariner, 
and it was not until this century that it was prosecuted for its own sake and 
elevated to the dignity of a geophysical problem by Humboldt and Gauss. 
A. Schuster: " Ueber die 26 tagige Periode meteorologischer Erschein- 
ungen." Repeatedly have investigators believed themselves to have discov- 
ered a twenty-six-day periodicity in meteorological and magnetic observations 

1 Sittungs-Berichte der Akademie der Wissenschaften zu Berlin ; math. phys. CI., 
1895, PP- 363-378. 



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NOTES 47 

due to the Sun's rotation. The author investigates theoretically the various 
errors to which one is liable in the search after periodicities underlying an 
irregularly running curve, and after a critical study comes to the conclusion 
that the investigations with respect to a twenty-six-day period thus far pub- 
lished cannot as yet be regarded as conclusive.' 

National Academy of Sciences of the United States of America, Washington , 
April, /Sqj. — "On the Secular Motion of a Free Magnetic Needle," by L. A. 
Bauer (introduced by C. Abbe), published in the Physical Review, Vol. 2, No. 
12, and Vol 3, No. 13. 

American Association for the Advancement of Science, Springfield, Mass., 
August and September, 1893. — F. H. Bigelow : "Solar Magnetic Radiation 
and Weather Forecasts," embodied in his paper " On the Status of the Solar 
Magnetic Problem," Science, October 18, 1895, p. 509; M. A. Veeder: 
" Magnetic Storms and Sun-spots, a Method of Showing Their Connection," 
privately published, Lyons, N. Y., August, 1895 » -£• ^» Bauer: "On the Dis- 
tribution and the Secular Variation of Terrestrial Magnetism," a paper giving 
the results of a communication to the Washington Philosophical Society, 
May, 1895, of which Nos. I., II. and III. have appeared in the American 
Journal of Science, August, September and October, 1895. The new 
chief of the United States Weather Bureau, Air. W % L. Moore, in his 
address before a joint meeting of the sections on the " Relations of 
the Weather Bureau to the Science and Industry of the Country," stated 
that Professor Bigelow's studies of terrestrial magnetic forces, as induced by 
the solar magnetic field, will be the line of investigation prosecuted during 
the next two years, from which it is hoped that results satisfactory to the 
practical as well as the theoretical man may be obtained." Results of these 
investigations are being published regularly in the Monthly Weather Review, 
edited by Professor Abbe. 

67. Versammlung Deutscher Naturforscher und Aerzte in Lubeck, Septem- 
ber 1893. Professor A. Paulsen : " Ueber die Natur des Polarlichtes ;" Profes- 
sor M. Eschenhagen : "Zum Studium der Variationen des Erdmagnetismus," 
to be printed in full in the second number of this Journal ; Professor G. 
Neumayer: " Der deutsche Plan flir die wissenschaftliche Erforschung der 
Slidpolar- Region"; Admiralitatrat Koldewey : " Ueber Construction und Pru- 
fung nautischer Instrumente, speciell der Sextanten und Com passe." 

British Association for the Advancement of Science, Ipswich, September 
1895. The President, Sir Douglas Dalton, in his inaugural address drew 
attention to the financial difficulties of the Magnetic Observatory at Falmouth, 
" close to the home of Robert Were Fox, whose name is inseparably connected 
with the early history of terrestrial magnetism in this country." ..." Cornish- 
men, indeed, could found no more fitting memorial of their distinguished coun- 
tryman, John Couch Adams, than by suitably endowing the Magnetic Obser- 

1 For further details, see the report of above meeting in the Mcteorologische Zeit- 
schrift, August, 1895. 




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48 REVIEWS [vol. I, No. ij 

vatory in which he took so lively an interest." The Journal hopes that this 
eloquent appeal will find a ready response. Before the Section of Physics, 
Professor Rucker presented two papers. The first gave the results of a com- 
parison of magnetic standard instruments, made by himself and Mr. W. 
Watson. It will be recalled that Professor Rucker in his presidential address 
before the Section last year emphasized the absolute necessity for an inter- 
comparison of the standard instruments at the various observatories in Eng- 
land on account of the instrumental differences shown to exist by his own 
investigations and previously by those of Rijckervorsel and Solander. During 
the past year the necessary observations have been made, a portable declin- 
ometer of the Kew pattern being carried to the various observatories. Accord- 
ing to Nature? "Errors are found in the latter [observatory standards] which 
are in every case traceable to magnetic material in or on the wooden box, 
containing the suspended magnet. If this box be replaced by an ebonite one, 
the error disappears. It is, however, easier to allow for the error than to get 
rid of it ; its amount is perfectly definite." In the second paper were com- 
municated the results of a test made at Rticker's instigation by Messrs. Kay and 
Whalley of the vertical (earth-air) electric currents revealed by Dr. Schmidt's 
(Gotha) re-computation of the Gaussian coefficients, preliminary results of 
which were presented to the society the previous year. " Such currents would 
be shown by the non-vanishing of the line-integral of magnetic force when 
taken round a closed circuit on the earth's surface. Four independent cir- 
cuits, three in Great Britain and one in Ireland, were taken and the data of 
magnetic force from the surveys of 1886 and 1891 were utilized. The results 
do not decide the general question, but they show that in the United King- 
dom the upward current has certainly not more than one-tenth of the value 
computed by Dr. Schmidt.* Lord Kelvin calculated that Dr. Schmidt's current 
(0.1 ampere per sq. km. of surface) amounts to a removal of the fine- weather 
charge of the air near the earth 36 times per second." Dr. Chree presented 
an elaborate paper which was adopted as the report of the committee on the 
Comparison and Reduction of Magnetic Observations, a review of which will 
be given in the second number. 

REVIEWS 

The Magnetic Observations Made at the Observatory at Batavia. Observations 
made at the Magnetic al and Meteorological Observatory at Batavia. 
Vol. XVI, 1893. Batavia, 1894. 
This volume may be regarded as the most important of this excellent 

series of publications, since it contains as a special feature, besides the usual 

September 26, 1895. 

* As the manuscript is passing through the press, Nature, December 19, brings an 
abstract of a paper by Prof. Rucker. on the same subject, which was read before the 
London Physical Society, December 13. Virtually the same conclusion was again 
reached. 



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REVIEWS 49 

annual records and results, a very full discussion of the observations during 
the period 1883 to 1893. 

This Observatory, which was established and is maintained by order of the 
government of Netherlands* India, was from its beginning, in 1867, placed 
in charge of Dr. P. A. Bergsma, by whom the first five volumes of records 
and results were published. Its position is in latitude 6° 11' oo'S and in 
longitude 106 48' 25 '.5 East from Greenwich. Temporary quarters were 
exchanged in 1879 f° r more permanent buildings, and about this time the 
old observations by eye were replaced by photographic registration, an Adie 
magnetograph having been set up in that year. Volumes VI-XVI were 
published by Dr. Van der Stok, who had been assistant director since 1877 
and who succeeded after Dr. Bergsma's death in May 1882, to the director- 
ship. 

The first volume appeared in 1871 ; it contains, besides records, discus- 
sions of the secular change, and of the diurnal, annual and semi-annual 
variations of the declination ; also investigations of the lunar-diurnal varia- 
tion, together with an analysis of the disturbances of the declination, the 
latter treated according to Sabine's method. 

This volume contains also a collection of values of resulting dips and of 
horizontal force component. 

The hourly records of the differential observations are fairly continuous ; 
the absolute determinations for declination, dips and intensity of the magnetic 
force, however, suffered some interruption in the earlier years. 

The special and most valuable feature in the volume mentioned at the head 
of this note, is the publication of the magnetic results obtained during the 
eleven years, 1 883-1 893, thus covering a sun-spot cycle. Its completeness 
may be judged by the fact that no less than seventy-three special tables are 
devoted to it. It should be remembered that the Author proposed to the Polar 
Conference at Vienna, a method of his own for the separation and discussion 
of the so-called disturbances ; all methods so far tried with more or less suc- 
cess, are laborious in application and of necessity must contain some arbitrary 
element. 

The investigation of the lunar influence upon the different magnetic ele- 
ments, the Author reserves for the next volume. 

C. A. Schott. 



LlZNAR, J. : Die Vertheilung der erdmagnetischen Kraft in Osterreich-Ungam 
zur Epoche i8go.o nach den in den Jahren i88g bis 1894 ausgefuhrten 
Afessungen. I. TheiL Erdmagnetische Messungen in Osterreich aus- 
gefiihrt auf Kosten der kais. Akad, d. Wiss. in den Jahren 1889-1893. 
Wien, 189s, 4°> 232 pp. and 1 fig. Repr. Denkschr. d. Wiener Akad. 
Math.-naturw. Ci. t Bd. LXIL 

This paper gives part of the results of a plan to repeat in Austria and 
Hungary the work of Karl Kreil who in 1 843-1 858 made an extensive mag- 



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SO REVIEWS [vol. I, No. i j 

netic survey of southeastern Europe, and at various points along the Asiatic 
coast. Kreil's measurements were reduced to the Epoch 1850.0, and the 
results with magnetic maps were published in the Denkschriften der mat hem. ~ 
naturw. CI. d. kais. Akad. d. Wiss. t Bd. XX. 

It was arranged that observations along the Adriatic coast should be in 
the care of the Hydrographic Office of Pola and that those in Hungary should 
be made by the kSn. Centralanstalt fUr Meteorol. u. Erdmagnetismus in 
Budapest. The stations of Kreil in other parts of Austria were taken by 
the Vienna Academy of Sciences. The instruments used by all observers 
included in this plan were compared'before and after the work of each year, 
and the observers in the field also made simultaneous observations at Pola 
and Trieste in the coast region, and at Budapest and 6-Gyalla in Hungary. 
In only rare instances was it found practicable to occupy the actual points of 
Kreil's observations, on account of modern industrial changes. 

The work described in the paper before us is the part retained by the Vienna 
Academy of Sciences, and placed in charge of the Author. The instruments 
used and the method of comparing them with those of the Centralanstalt fur 
Meteorologie und Erdmagnetismus in Vienna is fully explained, as is also 
the method of making the station observations, and of reducing them by 
means of the continuous records of the central observatory. 

The measurements of the horizontal and total intensity are in millemeter- 
millegramme-second units, so that the results are reduced to c. g. s. units by 
dividing by 10. 

The volume closes with a table giving the declination, inclination, hori- 
zontal and total intensity at each station together with its latitude and longitude. 
The stations number 109. 

F. E. Nipher. 



Die magnetischen Lokalabweichungen bei Moskau und ihre Beziehungen zur 
dortigen Lokalattraction. By Dr. H. Fritsche. Bulletin de la Soctiti 
ImpiriaU des Naturalistes de Moscou, No. 4, Annexe 1893, p. 381. 

Our knowledge of the interior of the earth is extremely limited, and the 
means of increasing it at present seem very inadequate in comparison with 
the interest of the questions involved. Even such fundamental problems as 
whether it is solid or liquid, and whether the external crust is rigidly sup- 
ported or is, so to speak, in a floating condition of equilibrium, are yet under 
discussion. The depths to which man has penetrated are as mere pricks and 
scratches compared with the size of the globe. A few experimental means 
are available for investigating to some extent the outer shell of the earth. 
Variations in the direction and amount of the force of gravity, as developed 
by geodetic operations, throw light on the density and condition of the por- 
tions nearer the surface, and irregularities in the magnetic elements, as 
measured instrumentally, are believed to be due to the presence of disturbing 
masses below and hence afford a means of studying the position and nature 



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REVIEWS 51 

of these masses. As indicated in the title, Dr. Fritsche in this interesting 
paper has endeavored to compare and show some relation between disturb- 
ances in the direction of the plumb line and in the magnetic elements, as 
observed in the neighborhood of Moscow. 

More than thirty years ago it was developed as a result of the geodetic 
triangulation of Russia and astronomical latitude determinations made in the 
vicinity of Moscow, that there is a considerable disturbance in the direction 
of the plumb line there. In a strip 180 kilometers long east and west and 
forty kilometers wide, including Moscow, the plumb line is deflected towards 
the north, with a maximum of eleven seconds of arc. About twelve kilo- 
meters south of Moscow there extends in W.S.W. and E.N.E. direction a line 
where the local attraction is zero, and the plumb line is normal to the mean 
spheroid representing the earth. South of this again is a region where the 
deflection is toward the south, with a maximum of about Ave seconds. The 
deflections in an east and west direction were not developed and are supposed 
small. So considerable a local attraction is unusual in so level a region as 
that surrounding Moscow. Schweizer, who discussed these plumb line dis- 
turbances, suggested several hypotheses to account for them, as that beneath 
the line of no local attraction there was an empty space, or a mass of much 
less density than that on either side. To see if any of this effect could be 
due to iron masses, and, if so, to investigate their position and size, Dr. 
Fritsche undertook, in 1893, a series of magnetic observations at thirty-one 
stations well distributed in the vicinity of Moscow and within a radius of 
eighty kilometers. As the whole work was done in eleven days, of course 
the most elaborate methods and instruments were not used, but all the ele- 
ments, declination, dip, intensity, both total and horizontal, were obtained at 
nearly all stations. The instruments, methods, and computations of the work 
are described with considerable detail. An azimuth compass was used for 
the declination observations, and the inclination and horizontal intensity were 
obtained with the compass by Lamont's methods. To compare the observations 
at the various stations, they were all reduced to the position of the observatory 
at Moscow by allowing for the normal variation of the magnetic elements with 
latitude and longitude as derived from a magnetic chart of European Russia. 
The difference, then, between the reduced values for each station and the 
mean for all thirty-one is taken as the anomaly for that station, and these 
values are tabulated, and are shown very clearly also on charts for each 
of the magnetic elements separately. For ready comparison the same 
charts exhibit the areas of plumb line deflection, and the line of no local 
attraction passing south of Moscow. There are also plotted the results of 
earlier magnetic observations in the vicinity of Moscow, more particularly 
those of Captain Meyen, made in 1853, which accord with the work of Dr. 
Fritsche. For the total intensity the chart shows a middle zone with a width 
of fifteen to twenty kilometers and a length of almost 150 kilometers from 
W.S.W. to E.N.E. (including the city of Mpscow) where the total intensity 
is considerably greater than the normal (maximum from 2% to $%), and beyond 



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52 REVIEWS [Vol. I. No. i] 

this zone both to the north and south it is less than normal. The dividing 
lines, or lines of no anomaly run on either side of Moscow and nearly parallel 
with the line of no deflection of the plumb line. To cause this effect on the 
total intensity the mass under the middle zone must be magnetized as the 
north pole of the earth, and the regions to the north and south must be oppo- 
sitely affected. The chart showing the anomalies in horizontal intensity is 
very similar to the preceding, save that the middle zone is somewhat further 
to the southward. In the grouping of the dip or inclination anomalies it is 
shown that there is a line of normal dip passing through Moscow in a W.S. 
W. and E.N.E. direction as before ; north of this line the dip is greater and 
south it is less than the normal, the maximum anomalies being about fifty 
minutes each way. The declination anomalies seem much less systematic 
than the others, but are grouped into a region northwest of and including 
Moscow with excessive western declination (maximum i° 35') and a region 
southeast where the needle is drawn abnormally to the east (maximum also 

i°35')- 

Dr. Fritsche's general conclusion is that these charts lead to the same 
result, that there are extended and connected disturbing ridges of iron 
beneath the surface, that below the middle zone being nearest the surface and 
charged with south magnetism, and the parallel ridges to the N.W. and S.E. 
with north magnetism though weaker than the middle one. The magnetiza- 
tion he attributes to the inductive effect of the earth's field. By comparing 
the position of the lines of normal dip and of normal horizontal intensity the 
estimate is made that the central disturbing mass is 10,700 meters below the 
surface. It is difficult to agree with Dr. Fritsche in his further suggestion that 
such a grouping of ridges of iron beneath the surface would also account for 
the plumb line deflections referred to. If as represented the central ridge of 
iron were nearer the surface and more massive than the others it would seem 
that the deflections should be toward it and not away from the central zone 
as the geodetic observations showed. In fact even if the three ridges were 
equal in mass and depth the deflections would in general be toward the center. 
That there is some relation between the magnetic and gravitational disturb- 
ances in this interesting locality however is indicated by the parallelism of 
the normal lines. It is possible that measurements of the force of gravity 
made in this vicinity might afford further information as to the conditions 
existing beneath the surface. If such iron masses as suggested existed with 
a density of nearly three times the average surface density they would 
doubtless have an effect on gravity which could be detected. When the 
general laws regarding the condition of the earth's crush are more fully 
established, it is probable that the remaining gravity anomalies may be 
studied with much value in connection with such local questions. Colonel 
Sterneck, in 1894, made pendulum observations at Moscow, but without a 
systematic comparison with results in other parts of Russia it is difficult to 
draw any inference at present. 

G. R. Putnam. 



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REVIEWS S3 

Die erdmagnetische Nachstorung. By Dr. W. van Bemmelen. Meteorolo- 
gische Zeitsckrift, September, 1895. 

This paper contains a brief summary of a computation whose purpose is 
to establish the direction from which the vectors of the forces distributing the 
normal magnetic field of the earth proceed. It is divided into two sections, 
(1) those pertaining to the disturbances taken day by day, and (2) those dis- 
turbing the field taken hour by hour, at a considerable number of stations. 
For the former case a series of about ten days in the neighborhood of a dis- 
turbance, the maximum impulse being near the middle, is selected, and the 
variations for H t D, V, taken on the monthly mean. These are reduced to 
units 6th decimal c. g. s. and the azimuth (N, W, S, E,) is completed at the 
several stations. It is suggested that better results would have been obtained 
by building a mean value for each day, on the assumption that the mean value 
for the month is true for the middle day, the 15th, and that the secular value 
of the field varies proportionately from the middle of one month to the middle 
of the next. Also it would have been more instructive to have computed the 
total vector s, and the altitude a, as well as the azimuth. Rectangular com- 
ponents contain the elements of useful knowledge, but it is more profitable to 
discuss them in polar vectors. Dr. van Bemmelen's conclusion is very 
important, namely that the vector meridians, which he calls " NachstSrung," 
lie orthogonally to the ovals of the auroral " isochasmen," with a pole nearly 
midway between the magnetic and the geographic poles. This construction 
agrees with that given by my own computations, the details being unpublished, 
from the results of which I was enabled to state that the disturbances come 
upon the Earth from north to south, and nearly in the planes of the magnetic 
meridians. Now this is true of the large, abnormal impulses, and also of the 
steady normal variations impressed upon the terrestrial field from day to day. 
Since it is desirable to distinguish these lines of impressed forces proceeding 
from extra-terrestrial sources, and because the directions are common to 
normal and abnormal disturbances (Nachstorung), would it not be acceptable 
to call them auroral meridians, as different from magnetic or geographical 
meridians? 

I am of opinion that the attempt to use quiet or steady days as reference 
for disturbances of an abnormal type is misconceived, that the available 
reference values are to be obtained by interpolation from monthly means, and 
that only barren results can be expected from computations referred to quiet 
days. The fact is that days of steady traces are disturbed in their means, as 
the unsteady days are, and the quiet traces sway up and down relatively to 
the base line, just like the abnormally unsteady days. This is of course to be 
modified in discussing hourly variations, where the diurnal rotation of the 
Earth has not eliminated the impressed forces of the equatorial field. 

The second portion of the paper continues the process for several stations 
taking now the hourly variations as the basis of investigation. The descrip- 
tion of the process of computation is very brief, but my impression is that the 
residuals are not quite pure. It is not enough to build the differences 



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54 PUBUCATIOXS [Voui.xo.ij 

between individual days and the analogous monthly means, bat for each day 
the normal mean must be obtained, and to that most be added the normal 
hourly variations, as given by the month, in order to secure a value from 
which to subtract the observed hourly value. However, it is shown that the 
impules in northern Europe crossed the magnetic meridians from northwest 
to southeast at an angle of 15*, which accords with my computation, the 
divergence changing at different stations. It is to be remarked that although 
the nadir component is more difficult to handle than the horizontal, yet it 
should be admitted to full play, if any expectation is entertained of arriving 
at the spatial location of the vectors of the impressed deflecting forces. 

Dr. van Bemmelen raises the question whether the axis of my coronal field 
at the Earth should make a daily movement about the geographical pole. 
Probably not, because the lines of force which at a distance from the Earth 
are nearly parallel to each other, are by the permeable nature of the Earth's 
shell greatly deflected, so that they sway about in space with the rotation of 
the Earth, the locus of contact at the surface not changing decidedly, though 
the angles may vary. The composition is, however, very fitful and fluttering, 
and until much more thoroughly studied, it is perhaps best not to attempt at 
present any final statement. The paper is very interesting and valuable. It 
is hoped that many investigators will be prompted to enter upon this fasci- 
nating field of physical research. 

F. H. Bigelow. 



PUBLICATIONS 

A number of valuable publications have been received, abstracts or 
reviews of which it was hoped it might be possible to insert in this number. 
In order not to delay the appearance of the Journal, however, it was neces 
sary to let them wait until the second issue. Nor will an attempt be made to 
give a list of recent works or articles, as the system of abbreviation for 
periodicals and publications is now under consideration. 



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TERRESTRIAL MAGNETISM 

AN INTERNATIONAL QUARTERLY JOURNAL 



volume i APRIL, 1896 




UEBER SIMULTAN-BEOBACHTUNGEN ERDMAGNE- 
TISCHER VARIATIONEN. 

Von M. ESCHENHAGEN IN POTSDAM. 

Als ein hervorragendes Ergebniss der ersten erdmagnetischen 
Forschungen Alexander v. Humboldt's und Arago's, sowie ins- 
besondere der Beobachtungen des von Gauss und Weber 
begrundeten magnetischen Vereins kann die Ermittelung der 
Gleichzeitigkeit des Auftretens gewisser starker Bewegungen 
der Magnetnadel an verschiedenen Orten gelten, und die magne- 
tischen Termincurven in den Tafeln der " Resultate des magne- 
tischen Vereins" fesseln noch heute wie damals das Auge durch 
das " Erkennen von Mass und Harmonie im anscheinend Regel- 
losen." 

Als im Jahre 1882-83 im System der internationalen Polar- 
forschung diese Terminbeobachtungen von neuem in bedeu- 
tendem Umfange angestellt wurden, ergab sich zwar auch fur 
verhaltnissmassig nahe, z. B. fur die europaischen Stationen, ein 
gleiches Resultat wie friiher, wahrend die ferneren und namentlich 
die den magnetischen Poien naheren Stationen erkennen lassen, 
dass wohl ein etwa gieichzeitiges Auftreten der magnetischen 
Storungen stattfindet, dass aber ein unmittelbarer Vergleich 
einzelner erdmagnetischer Ctfmponenten nicht mehr moglich ist, 
sondern dass diese plotziichen Variationen einem komplicirteren 
Gesetze gehorchen. Bei der Schwierigkeit, das umfangreiche 
Material, welches durch jene Terminbeobachtungen gewonnen 

55 



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56 M. ESCHENHAGEN [Vol. I. No. a] 

ist, zu bewaltigen, scheint es uns von Vortheil, erst mit einer ein- 
facheren Frage zu beginnen und nicht die grossen,verhaltnissmassig 
selten auftretendenStorungen, sondern die allerkleinsten, ziemjich 
haufig vorhandenen Bewegungen der Magnetnadeln zum Gegen- 
stande des Studiums zu machen. Eine Trennung der Storungen 
in Gruppen — wobei man zunachst an eine Eintheilung nach der 
verschiedenen Gr6sse denkt — scheint namlich zu dem Zwecke 
geboten, um zu erforschen, ob alle demselben Gesetze gehorchen, 
sich also z. B. nach Weltzeit richten, oder ob es Erscheinungen 
darunter giebt, die ortlicher Natur, wie z. B. die tagliche 
periodische Schwankung, oder die Einflusse der Gewitter sind. 

Nachdem man namlich seit 1858 (zuerst in England) ein 
photographisches Verfahren zur Registrirung der Schwankungen 
eingefuhrt und dasselbe im Jahre 1882 durch Anwendung des 
Bromsilbergelatinepapiers wesentlich vervollkommnet hatte, 
zeigen sich auf den in solcher Weise gewonnenen Curven, 
namentlich wenn die Linien hinreichende Scharfe besitzen, 
haufige, ganz kleine Wellen, die oft einige Zeit hindurch in nahezu 
gleicher Amplitude, zuweilen aber auch in wechselnder Grosse 
auftreten. Noch kleinere Wellen, deren Amplitude geringer als 
eine Bogenminute ist, gehen aber haufig durch die fiir solche 
Zwecke nicht hinreichend grosse Abscissen bietende Methode der 
Registrirung verloren. Um dieselben aufzuzeichnen, muss man 
wieder zu directen Scalenbeobachtungen greifen, wobei man 
einen photographischen Apparat anwenden kann, wie er von den 
Herren Schering und Zeissing in Darmstadt construirt worden ist, 
der zwar die photographische Curvenregistrirung nicht wird 
ersetzen oder verdrangen konnen, der' aber nach der angege- 
benen Richtung hin Vollkommenes leistet. Insbesondere ermdg- 
licht derselbe durch die pracise Zeitangabe die Losung der Frage, 
wie genau die Gleichzeitigkeit der Bewegungen der Magnet- 
nadeln bei grdsseren oder kleineren Storungen an verschiedenen 
Orten vorhanden ist. 

Die erwahnten alteren Terminbeobachtungen wurden an 
bestimmten Tagen von fiinf zu fiinf Minuten angestellt und nur 
im Polarjahre 1882-83 wurden auch Stunden verscharfter Beob- 
achtung mit Ablesungen alle zwanzig Secunden eingefuhrt ; 
hierdurch war es moglich, zu konstatiren, dass jene grossen 



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SIMUL TAN- BEOBA CHTUNGEN 5 7 

Storungen innerhalb eines Betrages von mehreren Minuten 
gleichzeitig an verschiedenen Orten auftreten — ein genaueres 
Resultat ergeben auch die photographischen Registrirungen 
nicht. 1 Fur eine vollkommen sichere Ermittelung reichen nun 
die Ablesungen aller zwanzig Secunden nicht aus, sondern man 
muss die Intervalle auf mindestens funf Secunden reduciren, 
ungefahr auch das ausserste, was von einem Beobachter, der 
zugleich Uhrzeit und Scalenablesung beobachten und protokol- 
liren soil, geleistet werden kann. 

Es wurden nun zum ersten Versuch solche streng simultane 
Beobachtungen nach mitteleuropaischer Zeit an den magne- 
tischen Observatorien zu Potsdam und Wilhelmshaven ange- 
stellt, und zwar versuchte man zuerst bei Gelegenheit von 
starkeren Storungen telegraphisch den Beginn der Beobachtung 
mitzutheilen. Doch es zeigte sich,dass es schwierig war, gerade 
eine gunstige Storung zu beobachten, da oft bei Empfang des 
Telegramms die Storung schon voruber war und es fur einen 
Beobachter zu anstrengend ist, die Ablesungen langer als eine 
Stunde fortzusetzeit. 

Man kam schliesslich (iberein, bestimmte Stunden zu ver- 
abreden, und wahlte die Abendstunde von 6 — 7, wahrend der die 
Storungen oder doch kleine, schnelle Bewegungen der Magnet- 
nadel haufig aufzutreten pflegen. Es wurde verabredet, die 
Ablesungen allein am Bifilarmagnetometer anzustellen, das sich 
auf beiden Stationen durch hohe Empfindlichkeit auszeichnet. 
Der Werth eines Scalentheils betrug rund 0,00003 C. G. S. 

Die an sechs Tagen eingehaltenen Terminstunden ergaben 
das Resultat, dass an den beiden 360 km entfernten Orten eine 
grosse Anzahl kleiner, ziemlich lebhafter Schwingungen, die 
man als bloss lokaler Natur anzusehen geneigt war, gleichzeitig 
auftraten. 

Indem man die so erhaltenen Ablesungen in Curven dar- 
stellte, (1 mm Abcisse = 5 sec, 1 cm Ordinate = 1 seal. = circa 
0,00003 C. G. S. a ) erkannte man, dass die grossere Anzahl von 

'W. Ellis, on the simultaneity of magnetic variations at different places 
on occasions of magnetic disturbance, and on the' relation between magnetic and 
earth current phenomena. — Proc. Roy, Soc. Vol. 52 1892. 

3 Um eine bequeme und kurze Bezeichnung der gemessenen Kraft zu erhalten, 
diirfte es sich empfehlen die Einheit der 5. Decimate der electrischen Einheit mit einem 



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i895> Marz 18, 


6 h. 7 h 


P 


.III., 


112 


19, 


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5 8 M. ESC HEN HA GEN [Vol. I . No. a J 

Wellen auf beiden Stationen gemeinschaftlich vertreten war ; der 
Vergleich der Zeiten der Umkehrpunkte ergab folgendes Resultat 
(n = Zahl der gemeinsamen Umkehrpunkte, P = Potsdam, 
W = Wilhelmshaven): 

n Different P—IV. 

+ 1.5 sec. 

- —3-3 

— 0.7 

- -2.3 

— 2.9 

- —0.9 

Um noch genauere Resultate zu erzielen wurde verabredet, 
die Zeiten der Umkehrpunkte direct aufzuschreiben, allein der 
Erfolg war kein wesentlich gunstigerer. Es ergab sich aus 1 2 1 
Umkehrpunkten einer Stunde die Differenz P-W = — 0.5 sec, 
welche Grosse als innerhalb der Beobachtungsfehler liegend 
bezeichnet werden muss, da die Einzelwerthe ahnliche Diffe- 
renzen aufwiesen, wie bei dem ersteren Verfahren. Man hat bei 
dieser Methode, die zwar bis zur grossten Genauigkeit ausge- 
bildet werden kann, den Nachtheil, dass aus Mangel an einer 
Curvendarstellung die Umkehrpunkte nicht immer sicher identi- 
ficiert werden konnen. 

Es scheint nach allem, dass man mit den beschriebenen 
Hiilfsmitteln auch die Gleichzeitigkeit nicht strenger als bis auf 
drei Secunden wird nachweisen konnen, so dass die oben gefun- 
denen Differenzen keinen sicheren Anspruch auf Realitat machen 
konnen, wie wir nachher noch genauer zeigen werden. Es ist 
dies auch nicht zu verwundern, wenn man bedenkt, dass manche 
Umkehrpunkte sich auf langere Zeitdauer, oft fiinfzehn bis 
zwanzig Secunden, erstrecken ; je scharfer die Umkehrpunkte, 
desto zuverlassiger stimmten dieselben aber auch uberein, so dass 
man vielleicht am besten thut, nur solche Daten auszuwahlen, 
wo die Magnetnadel ein bis auf funf Secunden scharf zu bestim- 
mendes Maximum oder Minimum besitzt. 

Man kann als das Ergebniss der bisherigen Beobachtungen 
feststellen, dass unter den vielen Zacken, welche die Tagescurven 
der erdmagnetischen Kraft an den beiden Stationen aufweisen, 

Buchstaben zu bezeichnen, z. B. mit dem griechischcn 7, wobei man sich des Namens 
Gauss erinnern mag, also 0.0000 1 C. G. S. = 7, damit ist zugleich die Grenze gekenn- 
zeichnet, wie weit ungefahr die Ermittelung der erdmagnetischen Kraft sicher ist. 



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SIMUL TAN-BEOBA CHTUNGEN 59 

keine einer rein lokalen Ursache zuzuschreiben ist, sondern dass 
sie wahrscheinlich in einem grossen Gebiet nahezu oder viel- 
leicht absolut gleichzeitig auftreten, und zwar bezieht sich dies 
sowohl auf die grossen Storungen, sowie auf ganz kleine Aende- 
rungen der Kraft, die nur etwa 3 y betragen. 

Bei der Wichtigkeit, welche diese Frage fur die Entdeckung 
der Ursachen der Storungen besitzt r ob dieselben namlich kos- 
mischer Natur sind, wobei Gleichzeitigkeit fur die ganze Erde 
stattfinden wurde, oder ob dieselben durch electrische Strome in 
den hoheren Schichten der Atmosphare bedingt sind, die ver- 
muthlich nur eine geringere oder gr6ssere lokale Wirkung haben 
wurden, schien es angezeigt, die Beobachtungen auf einige 
andere Stationen auszudehnen, ausserdem aber auch zu unter- 
suchen, von welchem Einfluss die Art des Instrumentes und der 
Beobachter ist. 

Es wurden zu dem Zwecke drei neue Terminstunden im 
Monat Juni letzten Jahres mit dem Observatorium zu Wilhelms- 
haven verabredet und das Marine-Observatorium in Washington 
gebeten, in der gleichen Weise zu beobachten. Die physikalisch- 
technische Reichsanstalt in Charlottenburg erklarte sich bereit, 
an einem der Termintage zu beobachten; auch die Betheiligung 
des Observatoriums in Gottingen wurde in Aussicht gestellt. 

In Potsdam selbst wurden zwei Instrumente zur Ablesung 
benutzt ; das eine war das friiher benutzte Bifilar (Edelmann'scher 
Construction), das andere war ein Unifilarmagnetometer, bei 
welchem ein an einem ziemlich starken Quarzfaden hangender 
magnetisirter Stahlspiegel durch Tordirung des Fadens senkrecht 
zum magnetischen Meridian gestellt wurde. Ein solcher Appa- 
rat — es wurde ein KohlrauscK sches Intensitatsvariometer von 
Hartmami und Braun ohne die vier kleinen Deflectoren benutzt — 
gestattet auch bei sehr kurzem Scalenabstande {% m) die Her- 
stellung einer hohen Empfindlichkeit. Wegen der kurzen 
Schwingungsdauer von circa drei Secunden des leichten Magnets 
und der vorzuglichen Beweglichkeit und guten Dampfung erschien 
es fur den vorliegenden Zweck besonders geeignet, wenngleich 
seine Brauchbarkeit fur langere Beobachtungsreihen hinsichtlich 
der Constanz der Null-Lage noch nicht erprobt ist. Die Schwing- 
ungsdauer beim andern Instrument (Bifilar) war circa fiinf bis 



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" "• 




" 12, 


Ferner : 


Juni II, 


Endlich : 


Juni II, 




" 12, 



60 M. ESCHENHAGEN [Vol. I. No. a] 

sechs Secunden, auch war es sehr gut gedampft, so dass hier die 
Gelegenheit sich bot, zwei ganzlich verschiedene Instrumente zu 
vergleichen. 

Bezeichnen wir das Bifilar mit Pi, das letztere Instrument 
mit Pn, ferner das Charlottenburger (ein Kohlrausch'sches 
Variometer mit vier Ablenkungsstaben) mit C, das in Wilhelms- 
haven mit W, so ergab sich folgendes Resultat : 

1895, J un > I0 » Pi— Pn — — 2.7 sec. aus 25 Umkehrpunkten. 
Pi-Pii= 0.0 " " 123 
Pi-P,i = -f z.o " " 124 
Pi- C = + 1.5 " " 43 
Pi-W =—0.8 " " 125 
P^W = — 5.2 " " 127 

In Potsdam waren die beiden Beobachter, am 10. und 12. Juni, 
in gleicher Weise vertheilt, am 1 1. Juni waren sie hingegen ver- 
tauscht, in Wilhelmshaven, wo der Termin vom 10. Juni durch 
Annaherung von eisernen Instrumenten unbrauchbar gewor- 
den ist, beobachtete stets der gleiche Beobachter, Herr 
Assistent E. Stuck, dem ich hiermit zu besonderem Danke 
verpflichtet bin. In Potsdam nahmen an diesen und den 
friiheren Terminen ausser dem Verfasser die Herren Dr. Arendt, 
Dr. Edler und Dr. Ludeling theil. Die Zeichnung der Curven 
ergab wiederum zum Theil recht gute Uebereinstimmung, wie ja 
auch die grosse Zahl der Umkehrpunkte beweist, die fur den 
Zeitraum von einer Stunde ganz betrSchtlich sind. Die Resul- 
tate im Verein mit den friiheren lassen zwar im Mittel einen 
messbaren Unterschied zwischen Potsdam und Wilhelmshaven 
bestehen, doch erscheint es, wenn man die Differenzen zweier 
Instrumente an demselben Orte vergleicht, zweifelhaft, ob der- 
selbe reell ist. Das gleiche gilt fur die Differenz Potsdam — 
Charlottenburg, bei welcher die geringe Zahl der Umkehrpunkte 
auffallt, da Charlottenburg eine etwas glattere Curve trotz 
gleicher Empfindlichkeit zeigt. 

Ganz anders gestalteten sich dagegen die Variationen in 
Washington. Freilich war das dortige Instrument um mehr als 
das doppelte unempfindlicher als die iibrigen, aber auch wenn 
man dies in Betracht zieht, so sind dort die Schwankungen ganz 
wesentlich geringer und anders geartet als an den deutschen 
Stationen. Zum Theil mag dies wohl dem Umstande zuzu- 



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SIMUL TAN- BEOBA CHTUNGEN 6 1 

schreiben sein, dass man bei so entfernten Stationen nicht nur ein 
Element vergleichen darf, sondern mindestens beide horizontale 
Componenten heranziehen muss, immerhin aber ist es auf- 
fallend, dass dort gar nichts von den verhaltnismassig lebhaften, 
wenn auch kleinen Schwankungen der deutschen Stationen zu 
erkennen ist. 

Es bedarf dies Ergebniss einer mehrfachen Nachprufung, wie 
insbesondere durch Ausdehnung auf zahlreichere Stationen. 
Es besteht daher die Absicht, derartige Stunden verscharfter 
Beobachtungen in regelmassigen Intervallen international vor- 
zuschlagen, in der Hoffnung, dass sich eine genugende Anzahl 
von Beobachtern findet. Fur Deutschland hat es ein besonderes 
Interesse, an einer Anzahl von gunstig vertheilten Stellen dieses 
Landes die Beobachtungen durchzufiihren, da es fur eine etwaige 
detaillirte Landesaufnahme Bedeutung hat, die Art der geogra- 
phischen Verbreitung der Variationen zur Ableitung der 
Reductionselemente auf eine einheitliche Epoche zu gewinnen. 
Gelingt es, eine internationale Betheiligung an derartigen Beob- 
achtungen in ahnlicher Weise wie es vor 50 — 60 Jahren der Fall 
war, zu erreichen, so durfte, abgesehen von den directen Resul- 
taten, ein Nutzen fur die erdmagnetische Wissenschaft auch 
dadurch zu erzielen sein, dass ein gemeinsames Arbeiten sowie 
ein Austausch von Aufzeichnungen etc., was unbedingt noth- 
wendig ist, angebahnt wird. 1 

1 Vorstchendes ist der wesenUiche Inhalt eines vom Verfasser auf der " Ver- 
sammlung deutscher Naturforscher und Aerzte " zu Lubeck im September 1895 gehal- 
tenen Vortrages. Eine Anregung zur Anstellung der Simultanbeobachtungen ist 
inzwischen von dem Director des Kgl. Meteorologischen Instituts, Dr. von Bezold, 
durch Circulare an eine kleinere Anzahl Magnetischer Observatorien ausgegangen. 
Die Beobachtungstermine sind : 

Februar 27. 5-6 p.m. MitU. Zeit Greenwich 

28. 6-7 " 
Marz 12. 5-6 " 
13. 6-7 " 
Es sollen moglichst Declination und Horizontal-Intensitat alle fiinf Secunden 
abgelesen werden. Im Fall die Ergebnisse zur Fortsetzung ermuthigen, werden dem 
im September d. Y. in Paris zusammentretenden Congress der Directoren Meteoro- 
logischer Observatorien Vorschlage unterbreitet werden. 



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THE SECULAR VARIATION OF THE DIRECTION OF 
A FREELY SUSPENDED MAGNETIC NEEDLE AT 
CALLAO, VALPARAISO, SHANGHAI, HONGKONG, 
AND SYDNEY. 

By G. W. Little hales, 
Washington, D. C. 

The object of this paper is part of a general purpose to col- 
lect and present from time to time the recorded observations of 
the magnetic declination and dip at stations in all parts of the 
world, with a view of amplifying the investigations that have 
already been made into this subject and thus preparing the way 
for throwing more light upon the question of the periodic nature 
of the secular variation of the magnetic needle. 

The collections of data relating to Callao, Valparaiso, Shang- 
hai, Hongkong, and Sydney are here presented together with 
the results obtained by adapting formulas of interpolation to the 
observations. And the curves traced out by the north end of 
the needle upon planes tangent to the sphere in latitudes corres- 
ponding to the mean values of the dip at the various stations are 
also given in accordance with the method employed by Dr. L. A. 
Bauer. 1 Attention is especially invited to the new case presented 
at Sydney, where the needle has receded, since i860, over the 
path along which it passed prior to that year. 

Table I gives a comparison of the observed and computed 
values of declination and inclination ; and also the date, observer, 
and source of each observation used in the discussion. 

Table II gives the empirical expressions arrived at by treat- 
ing the observations by the method of least squares. The col- 
umn Epoch gives the date of the first and last observation used 
in deducing the empirical equations. The column r gives the 
probable error, in minutes, of a single observation. The column 

1 In his Beitrdge zur Kenntniss des YVesens der Sdcular- Variation des Erdmagne- 
tismttSy Berlin, 1895. 

62 



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SECULAR MOTION OF FREE MAGNETIC NEEDLE 63 

P gives the period which was assumed in the investigation where 
the form of the equation was not assumed to be parabolic. The 
weight assigned to the observations in each of the computations 
is unity, except in deriving the declination equation for Hong- 
kong in which case the weights are given in Table I. 

Table III gives the data for constructing the secular curve. 
D represents the declination, plus when the north end of the 
needle points west of true north and minus when it points east. 
I stands for the inclination, plus when the north end of the needle 
is below the horizon and minus when it is above. 

The curves are traced in each case upon a gnomonic projec- 
tion whose point of tangency has for its latitude, 7 , the mean 
of the extreme values of the inclination during the epoch for 
which the curve is constructed, and for its longitude, D Q , the 
mean of the extreme declinations. 

The sphere to which the planes of projection are tangent 
has a radius of twelve inches, this being one-half the length of 
the needle. 1 

The projections upon which the curves are drawn were con- 
structed graphically according to the method shown on p. 70. 

Abbreviations Used in Designating Source of Observed Elements : 

Adventure, Voyages of the Adventure and Beagle, 1826-36, London, 1839. 

Annalen, % jj, Annalen der Hydrographie, 1877. 

Annales, '76, Annales Hydrographiques, 1876. 

Annates, '84, " " 2d series, 1884. 

Annales, 1, '92, " " " 1st vol., 1892. 

Annales, 2, '92, " " " 2d vol., 1892. 

Annales, 2, '93, " " " 2d vol., 1893. 

Archives, Manuscript deposited in the Archives of the Hydrographie Office, 
Washington, D. C, U. S. A. 

Becquerel, Becquerel's Traite" du Magnetisme, 1846. 

Bode, Bode's Astronomisches Jahrbuch, 1828. 

Brewster, Brewster's Treatise on Magnetism, Edinburgh, 1 837. 

Challenger, Report of Vogageof H. M. S. Challenger. 

Doberck, Observations and Researches at Hongkong, by W. Doberck ; pub- 
lished annually since 1885. 

1 In the work cited, Bauer supposed the half length of the needle to be 20 cm. In 
his article in the Physical Review, Vol. II., p. 455, and Vol. III., p. 34, his curves were 
reduced so that the half length of the needle would be' six inches. Hence, my curves 
are on twice the scale employed in this latter paper. 



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64 



G. IV. L1TTLEHALES 



[Vol. I. No. aj 



Hansteen, Hansteen's Magnetismus der Erde, Christiania, 1819. 

Hongkong, Observations and Researches at the Hongkong Observatory, 1885 

(Appendix A). 
Hydrogr., 109, Hydrographic Office (U. S. A.), publication No. 109. 
Petermann, Erganzungsheft No. 77 1 zu Petermann Mittheilungen, Band XVII., 

1884-5. 
Smithson., 239, Smithsonian Contributions to Knowledge, No. 239, 1 873. 
Trans., I., 1875, Philosophical Transactions of the Royal Society, Part I, 1875. 
Trans., I., 1877, Philosophical Transactions of the Royal Society, Part I, 1877. 
Trans., II., 1877, Philosophical Transactions of the Royal Society, Part II, 1877. 
Zi-Ka-Wei, " The Meteorological Elements of the Climate of Shanghai, 

Zi-Ka-Wei Observatory," 1885. 
Zi-Ka-Wei, '76, Report for 1876 of the Zi-Ka-Wei Observatory. 

Table I. 

COMPARISON OF OBSERVED AND COMPUTED ELEMENTS. 



Date 



1709.C 
1802 
1823 
1827 

IS35 
1836 
1838 
1858 
1866 

1883 
1892 

1893 



1790 
1823 
1835 
1838 
1838 
1858 
1866 
1893 



Observer 



Source 



CALLAO, PERU. 
Lat. 12° 04' S. Long. 77° 08' W. of Gr. 



DECLINATION. 



Feuille*e . 



Friesach 



Ensg. Favereau, Fr. N. 
Lt. W.Conway, U.S.N. 
Lt. L. Mottez, Fr. N 



Hansteen . 
Becquerel. . 
Adventure . 



Trans., II., 1877.. 



Annales, '84 . . . 

Archives * 

Arnales, 2, '93 . 



INCLINATION. 



Don Malaspina 

Duperrey 

Fitz Roy 

Belcher , 

La Venus 

Friesach 

Harkness 

Lt. Mottez, Fr. N 



Bode 

Adventure . 



Trans., II., 1877. 



Annales, 2, '93. . 



Observed 


Computed 


- 6°.2 5 


— 6°.32 


- 9 .83 


— 9 52 


— 9 .50 


— 10 21 


— 10 .66 


—10 .31 


— 10 .60 


—10 .47 


—10 .40 


—10 .49 


—10 .50 


—10 .51 


— 10 .66 


— 10 .60 


— 10 .50 


—10 .53 


— 9 -97 


— 10 .19 


—10 .00 


— 9 .91 


— 10 .00 


- 9 .87 


— 12.°37 


— 12°. 17 


-8. 55 


-8 .34 


— 7. 05 


— 7 .37 


— 6. 23 


- 7 .16 


— 6. 82 


- 7 .16 


— 7- 17 


— 6 .12 


— 6. 47 


— 5 .86 


— 5- 25 


— 5 .75 



O.-C. 



-f-o°.07 
— o .31 
+0 .71 
— o .35 

+0 .09 
+0 .01 
— .06 
+0 .03 

+0 .22 

— o .09 
—0 .13 



— o\ao 
— o .21 
+0 .32 
+0 93 
+0 .34 
—1 .05 
—0 .61 
+0 .50 



1 Hydrographic information from U. S. S. Yorktown. 



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SECULAR MOTION OF FREE MAGNETIC NEEDLE 



65 



Table I. — Continued. 



Date 



1709 
1744 
1793 
1802 
1821 
1823 
1825 
1831 
1835 
1837 
1838 

1859 
1866 
1882.6 

1883.2 

1884 



1790 
1827 
1830 

1835 
1836 

1837 
1838 
1838 
1852 
1859 
1866 
1868 

1875.9 
1875.9 
1893.O 



Observer 



Source 



VALPARAISO, CHILE. 
Lat. 33 02' S. Long. 71 ° 39' W. 



DECLINATION. 



Feuillce 



B.Hall 

Morrell 

Beechey 

King 

Laplace 

Beechey 

La Venus 

Novara Expedition . . 

Harkness 

Lts. Barnadieres and 

Barnaud, Fr. N . . 
Lts. Barnadieres and 

Barnaud, Fr. N . . 
Lt. J. W. Carlin, 

U. S. N 



Trans., II., 1877 . . 
Adventure 



Becquerel 

Trans., II., 1877 



Smithson., 239 

French Mag. Survey 

Annales, 1884 

Hydrogr., 109 



INCLINATION. 



Don Malaspina. 

Liitke 

King 

Fitz Roy 

Beechey 

La Venus 



Swed. Mag. Survey.. 

Novara Expedition. . Trans., II., 1877 

Harkness 

H. M.S. Nassua.... 
Nares and Thompson 



Lt. Mottez, Fr. N. . . 



Bode 

Trans., II., 1877 



Annalen, '77 . . 



Challenger 

«< 

Annales, 2, '93 



Observed 



- 9"-50 
-12 .50 
-14 .82 
-14 .92 
-14 .72 

-15 .68 

-15 .87 

-15 .00 

-15 .30 
-15 .58 

-15 .60 
-15 .67 
-15 .85 

-15 .43 

-15 .25 

-15 .68 



-44°96 
-39 .10 
-40 .19 
-38 .05 
-37 .08 
-38 .33 
-38 .72 
-38 .20 
-36 .80 
-35 .67 
-35 .38 
-34 .38 
-33 -79 
-32 .57 
-31 .83 



Computed 


O.-C. 


— io'\ 24 


+o°.74 


—II .98 


—0 .52 


-14 .38 


—0 .44 


—14 .76 


— .16 


-15 -39 


+0 .67 


-15 -44 


—0 .24 


-15 -49 


—0 .38 


—15 .61 


+0 .61 


—15 .67 


+0 .37 


-15 .69 


4-o .11 
+0 .09 


-15 .69 


-15 .72 


+0 .05 


-15 .63 


— .22 


—15 -24 


— .19 


-15 23 


— .02 


— 15.21 


—0 .47 


— 44°-76 


— 0°.20 


—39 -73 


+O.63 


—39 .31 


—0 .88 


—38 .60 


+0 .55 


-38 .45 


+1 -37 


-38 .32 


— .01 


-38 .17 


—0 .55 


-38 .17 


—0 .03 


—36 .32 


—0 .48 


—35 .40 


— .27 


—34 .56 


—0 .82 


—34 -33 


—0 .05 


—33 .49 


—0 .30 


—33 .49 


+0 .92 


—32 .04 


+0 .21 



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66 



G. IV. LITTLEHALES 



[Voi- I, No. a J 



Table I, Continued. 



Date 



Observer 



Source 



SHANGHAI, CHINA, 
Lat. 31 15' N. Long. 121 29 K. 

DECLINATION 



1858 

1875 
1876 

1877 
1878 

1879 
1880 
1881 
1882 
1883 
1884 



1843 

1858 

1872.3 

1873.3 

1875.5 

1876.5 

1877.5 

1878.5 

1879.5 

1880.5 

1881.5 

1882.5 

1883.5 

1884.5 
1890 



Novara Expedition 
Jesuit Missionaries, 



Trans., I, 1875. 
Zi-Ka-Wei.... 



Inclination. 



Sir E. Home 

Novara Expedition. 
Shadwell 



Jesuit Missionaries.. 



Zi-Ka-Wei, '76. 
Trans., I, '75.. . 

" " 77- • 



Zi-Ka-Wei . 



Observed Computed 



+ i c .«3 
+ 1 .98 
+2 .02 

-f 2 .02 

-j-2 .00 
-j-2 .02 
t-2 .03 
+ 2 .05 
+2 .09 
+2 .08 
+2 .13 



4475 
45.35 
46.24 
46.32 
46.26 
46.23 
46.23 
46.22 
46.25 
46.27 
46.28 
46.30 
46.32 
46.32 
46.19 



O.C. 



+I.92 

-f2 .00 
-4-2 .01 
+2 .02 
-* 2 .02 
+2 .03 
+ 2 .04 
+ 2 .05 
-*-2 .00 
+2 .07 
+2 .08 



44.72 
45.70 
46.I7 
46.20 
46.23 
46.23 
46.25 
46.25 
46.27 
46.27 
46.26 
46.27 
46.26 
46.25 
46.I9 



- 


.<*> 


— 


.02 


- 


.01 





.00 


— 


.02 


- 


.01 


— 


.01 





.00 


- 

+0 


•03 
.01 



.05 



-0.03 

-o.3S 
^0.07 
—0.12 
-ro.03 

0.00 
- 0.02 
—0.03 
— 0.02 

0.00 
-+ 0.02 
+0.03 
+0.06 
+0.07 

0.00 



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SECULAR MOTION OF FREE MAGNETIC NEEDLE 
Table I, Continued. 



67 



Date 



I78O 

1792 

1824 

1827 

183O 

1837 

1843 

1855 

1875 

1876 

1884 

1885.5 

1887.5 



1791 
1827 

1837 

184I.I 

1843 

18438 

1851 

1858 

1858. 1 

1872.3 

18733 

18743 

1875 

1875 

18757 

1884.5 

1885.5 

1886.5 

1887.5 

1888.5 

1889.5 

189O.2 

1891.3 

1 89I.8 

1892.5 

1893.5 
1894.5 



Observer 



Source 



HONGKONG, CHINA 

Lat. 22° 16' N. Long. 114 10' E. 

Declination. 1 



Cook. 



Bougainville. 
Beechey .... 
Laplace .... 
Darandeau .. . 

Belcher 

Richards. ... 



Doberck . 



Hansteen 

Brewster 

Becquerel 

Trans., I., 1875. 



Hongkong . 



Annates, '76. 
Hongkong. . , 



Doberck . 



Inclination 



Don Malaspina 

Beechey 

Darandeau 

Observatory 

Belcher 

Observatory 

Co 11 in son 

Novara Expedition.. 

Observatory 

Shadwell 

Nares & Thompson. . 

Fritsche 

Observatory 

a 

•< 

Lieut. deRoujon,Fr. N. 

Observatory 

Lieut.DHMahan,USN 

Observatorv 



Bode 

Trans., I., 1875 
u •» 

Hongkong. . . . 
Trans., 1., 1875 

Hongkong 

Trans., I., 1875 

Hongkong . 

Trans., I., 1877 

Challenger. . . . 

Petennann 

Doberck 

•« 
u 

Annales, 1, '92 

Doberck 

Archives 

Doberck 



Observed 



Computed 



4 0^.50 


1 
— o°.48 


—1 .28 


—0 .70 


— 1 .70 


—1 .06 


— 2 .00 


-1 .08 


-1 .58 


—1 .08 


—1 .08 


—1 .09 


— .62 


-1 .08 


— .50 


—1 .03 


— .93 


—0 .80 


—0 .60 


- .79 


— .77 


—0 .65 


— .75 


—0 .62 


— .70 


—0 .59 


27.92 


26.99 


29.97 


29.89 


30.53 


30.18 


30.05 


30.44 


30.05 


30.58 


30.83 


30.59 


29.67 


30.99 


3i.i3 


31-34 


31.10 


31-35 


32.30 


3I-9I 


32.33 


3L9I 


32.29 


31.98 


32.34 


32.00 


32.30 


32.00 


31.95 


32.02 


32.45 


32.23 


32.44 


32.26 


32.43 


32.27 


32.37 


32.29 


32.35 


32.31 


32.28 


32.32 


32.17 


32.34 


32.40 


32.35 


32.08 


32 35 


32.05 


32.36 


31.95 


32.37 


31.88 


32.38 

1 



o.-c. 



fo.98 
—0.58 
— 0.64 
—0.92 
— 0.50 

4-0.01 

4-0.46 
-0.53 
—0.13 

T 0.19 
— 0.12 

—0.13 
— 0.1 1 



tO*.93 
4-o .08 
■fo -35 
— o .39 
-o .53 

T .24 

—I 32 

— .21 

— .25 

4-0 .39 

4-0 .42 
— o 
t o 
-0 



- 

-o 

+0 
fo 



•31 

34 

30 
07 

.22 

,18 
.16 
.08 



4-o .04 
— .04 
— o .17 
; .05 
—0 .27 
— o .31 
— o .42 
— o .50 



■ The weights assigned to the observed quantities were as follows : one-fourth to 
the first, second and fourth observations, one-half to the second, fifth and sixth, and 
unity to the remainder. 



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68 



G. W. LITTLEHALES 
Table I. — Concluded. 



[Vol.. I, Xo. 2 j 



Date 



Observer 



Source 



1770 
1787 
1 793-2 
1803 
I8I3 

1818.5 



1823 

184I 
1844 
1848.5 

I85I.5 

1858 
1864 
1866.5 

1872 
1875 
1880 



1793.2 
1824 

1831 
1837 

1841 

1 844 

1849 

1852 

1858 

1874.4 

1890.8 



SYDNEY, AUSTRALIA. 
Lat. 33 52' S. Long. 151 ° 12' E. 

DECLINATION. 



Cook. . . 
Hunter 



»— 8 



Flinders 

Brewster 

-8°.70 Capt. King, 1817.7. . 

.93 Freycinet, 18 19 

*— 8 .81 Brewster, 1822 

-8 .80 Rumkerand SirT. 
Brisbane, 1823... . 

-8 .93 Brewster, 1824 

\ — 9°.85 Erebus, 1 84 1 

>— 9°.95 SirJ. C. Ross,i84i.. 

H. M.S. Fly 

f— io°.o8 Rattlesnake, 1848.. 
> — 10M5 " 1849-- 

j — 9°-72 Admiral King, 185 1 
(— 9°.8o " " 1852 

Capt. Denham 

Smalley 



1 -1 

1= 



9°. 62 Russell, 1870 

9°.58 " 1871 

9°.57 " 1872 

°.53 " 1873 

9°.55 " 1874 

9°.47 H.M.S.Chal'ger/74 

9°.55 Russell, 1875.5... 



— 9°.53 
~9°.58 
— 9°.6o 
— 9°. 60 
— 9°. 60 



1878. 
1879. 
1880. 
1881. 
1882. 



Don Malaspina 

Duperrey 

;— 62°.88 Bethane, 1831 

1 — 62°.85 Dunlop, 1831 

[— 62°.82 Fitz Roy, 1836.... 

— 62°.8o Anonymous, 1837.. 

— 62°.85 Wickham, 1838.... 
^—62°. 98 H. M. S. Terror, '4 1 



— 62°.8o 

— 62°.87 

—62 . 70 
' — 62 .62 
| -62 .75 

—62 .52 
' 62 .73 

Kerr 

Novara Fxpedition 

Challenger 

Lt. Courmes, Fr. N 



Erebus, 

Terror, " 

Erebus, " 

Fly 1842 . 

" 1844 . 

" 1845. 

Rattlesnake 



Adventure . 



Brewster . . 
Adventure . 
Archives . . 



Adventure . 
Archives . . 



Trans., II., '77. 

Archives 

Trans., II., '77- 



Archives * . 



INCLINATION. 



Bode 

Trans., II., 1877 



Challenger 

Annales, a» '92 



Observed 


Computed 


— 8" 


.00 


— 7° 


.82 


- 8 


.50 


— 8 


•35 


— 8 


•77 


— 8 


•53 


— 8 


.85 


— 8 


.82 


— 8 


.87 


— 9 


.08 


— 8 


.78 


— 9 


.22 


— 8 


.83 


— 9 


.32 


— 9 


.90 


— 9 


.62 


— 9 


.42 


— 9 


.63 


—10 


.12 


— 9 


.68 


— 9 


.76 


— 9 


.70 


- -10 


.00 


— 9 


•73 


— 9 


.82 


— 9 


.72 


— 9 


72 


— 9 


•72 


— 9 


•57 


— 9 


.70 


— 9 


.52 


— 9 


.67 


— 9 


.58 


— 9 


.60 


—60 


.01 


— 60 


.03 


—62 


.31 


—62 


.17 


—62 


.86 


—62 


•47 


-62 


.82 


—62 


.69 


—62 


.84 


—62 


.80 


—62 


.63 


—62 


.87 


—62 


•73 


—62 


.96 


—62 


•73 


—62 


•99 


—62 


.68 


~63 


.04 


—62 


.76 


—62 


.91 


—62 


.07 


-62 


.42 



o.-c. 



— o\i8 
— o .15 
— o .24 
— o .03 

+0 .21 

+0 .44 



-ho .49 
— o .28 

+0 .21 

— O 44 
— .06 

— .27 

— .10 

o .00 

+0 .13 
+0 .15 

+0 .02 



+0 .02 

— .14 

— o .39 

— o .13 



.04 



+0 .24 

+0 .23 
+0 .26 
-ho .36 
-fo .15 
~o .55 



1 A letter from director of Government Observatory at Sydney, dated i860. 



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SECULAR MOTION OF FREE MAGNETIC NEEDLE 



69 



3 £.5 

OQ . O 






OQ 



1 1 jl i 

O O «-■ en O 



M 4* ON 



1 jl jl 

o o •■* en o 

"^ 00>b On 4k M 

1 T * 



I. 



o 

ON ON 



I Jl J, 

O O K» Cn O 



N ON 

1 T 



II M 

CO MUiO 



I I 



II II 

<OOMAO 
o 

nu ia on on „ 

i 1 l ? 

O^U> 4* U> 



I I 



J, I 

4*. O 



J, » 

en O 



on 4k 

I I 

4* 

o 00 
o 



11 jl 1 

; b i h m M 

I lis 

0^U> 4k cu 
|m Mm m on 



> ^J en 

> KJ 4k 

I I 



C MO Qsu> 



I I 



SSS88 

1 I I 

0>U> Au h 

- O en 00 O S* 

9§bbb 
OOOOO 



0>Ui 4k 



« en O 

> "^ on 

on »i 

JJ 

O^ ON 



> 

o 
po 

O 

o 
ss 
Hi 

H 

PC 

a 
o 

H 

s 

a 

H 

K 
W 

tfi 

w 
o 

a 
r 
> 
po 

o 
a 

< 



> 
cs 
r 
w 



s 



O 



o 

s 

OQ 



ST p 

a T3 

0Q P 

p S. 



~ 


C 


1 


II 


I 

ON 


1 

00 


K> 













O 


K> 


A 





II II _H II II II II II 

M oO» o I I I I 

.°o .°o^ '-' °" 00 

OOvO ~ ~ O W . ° o 

nTw I .<».'* i. 

_i_~T"_i 1 O ON ON en 

°^ o . ° O 






+ 



O 

o> 

.en M °l^^lO h i'* ^ 



o O^i— 1 i-i 
' k. ' — '. 00 



-Se^ 
•» o 



.<*> ; 



«vi «»a «vi «vi 00 oo«vi «vi «vi *a 




OM€ 


0C4* en 




U> O 

1 1 


1 


O u> 

1 1 


oco 

1 1 1 




1- 1 


f 


00 oc 
vO oc 


ococooooococococ 


=r 





oco 


oco oco 




l~ 


-U 


^J O 4k U> *k U> U> 




lilt 


If 


'+• 1+ if If 1+ 


:nt 










K> i-i 


-K> ~ 




u» 


OCen 4k 


h ocoo 


1-1 M 


" 


b 4*. 





b en 


on b b 


b k> 




• U> 4k 


4k • 


• 4k es> 


• u> 




• to 


O en • 


. On 


• 


*tf 


• 





• 


• 


• 





5? 

a 
w 



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70 



G. IV. LITTLEHALES 



[Vol. I, No. a J 



GRAPHICAL CONSTRUCTION OF THE GXOMONIC PROJECTION 




T = point of tangency 
DE = B E , EF = E F , etc. 

BK = B K\ LK = L'K',etc. 

AP- = A P\ AO, =A 0\ etc. 

CT = radius = ) z length of needle 



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SECULAR MOTION OF FREE MAGNETIC NEEDLE 
CALLAO HONGKONG 



7' 



















rr 
















»* 
















iK" 
















\*S 














!»' 
















«• 




























































im 


> 
















In 


» 
































3 


r 


b 
















■$ 
























e 


r i 


§• i 


* 


Jb* 


!• 


A 1 


4 i 


c 




SHANGHAI. 



VALPARAISO. 




SYDNLY 



Jaors 



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72 COMPARISON OF MAGNETIC INSTRUMENTS [Vol. I. No. a] 

[Interim Report of the B. A. A. S. Committee, consisting of Professor A. 
W. Riicker (Chairman), Mr. W. Watson (Secretary), Professor A. Schuster, 
and Professor H. H. Turner, appointed to confer with the Astronomer Royal 
and the Superintendents of other Observatories with reference to the Compari- 
son of Magnetic Standards with a view of carrying out such Comparison. Pre- 
sented at the Ipswich meeting, 1895.]* 

Professor ROcker and Mr. Watson have carefully compared 
three Kew-pattern magnetometers in order to investigate the 
causes of the discrepancies between the measurements of decli- 
nation made with them. They find that if the greatest care be 
taken in the manufacture of the wooden box and the metallic 
adjuncts which are close to the magnet the discrepancies dis- 
appear. 

In other words, the cause of the difficulty, in these three 
instruments at all events, is, not the metal base, but the much 
smaller masses of metal which are nearer to the magnet. 

The three magnetometers are now in good accord. 

A week has been spent at each of four observatories for the 
purpose of comparing one of these magnetometers and a dip- 
circle with the observatory instruments. Professor Riicker made 
the observations at Kew and Falmouth ; Mr. Watson, those at 
Stonyhurst and Valentia. 

The greater part of the work which the Committee undertook 
has thus been accomplished. 

It is still necessary to compare the instruments again with the 
instruments at Kew to ascertain that they are unaltered by trans- 
fer from one place to another ; and as a new magnet-house is 
about to be built at Greenwich, it has been thought better to 
postpone the comparisons at that Observatory until the house is 
ready for use. 

The reductions of the observations which have been made 
are not yet finished. A full report will be made when the work 
is completed. 

The Committee therefore ask to be reappointed, but no 
further grant is required. 

1 Owing to incomplete information at hand, the brief account of this report given 
on p. 48 in the first number of this Journal contained some inaccuracies. Having 
received in the meantime from the secretary the printed report, we are glad to be able 
to reprint it entire. — Ed. 



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LOGARITHMEN DER KUGELFUNCTIONEN DER ERSTEN 
FtTNF ORDNUNGEN VON FUNF ZU FUNF GRAD. 

Von Dr. Ad. Schmidt (gotha). 

In der von mir im ersten Hefte dieser Zeitschrift mitgeteilten 
Untersuchung habe ich (S. 20) anstatt der gewohnlich benutzten 
Kugeifunctionen gewisse Vieifache davon angewendet, die ich 
RZ nannte und durch die Gleichungen 



m <i m P M U) 

mit r?(p) = (i — n 2 P -^r-^^ = cos«, c =i, € x = €,= . . =2 
definierte. 

Die Vereinfachung, die bei der dort behandeiten Aufgabe die 
analytische Entwickelung dadurch erfuhr (wobei ubrigens der 
Factor (2/1 + 1) ohne Bedeutung war), hatte nicht hingereicht, 
die Abweichung von den ublichen Bezeichnungsweisen zu recht- 
fertigen. Was mich bereits an einer anderen Stelie zur Einfiih- 
rung der Functionen R£ veraniasste und was mich ihre aiigemeine 
Verwendung hier befiirworten lasst, ist der Vorteil, den sie in 
numerischen Entwickeiungen gewahren. 

Die einzelnen Functionen P* und T% sind von merklich ver- 
schiedener Grossenordnung ; so sind die Maximalwerte von P\ % 
P\ % P\, PI P\ gleich 1, 0.275, 1, 0.082, 1, diejenigen von T\ t T l v 
7*J, T\, T\ gleich 1, 2.06, 15, 3.23, 945. Die einzelnen Glieder 
einer nach diesen Functionen entwickelten Reihe sind daher 
bei gleicher Grosse ihrer Coefficienten von sehr verschiedener 
Bedeutung, was schon in diesem einfachsten Falle und noch 
mehr bei beliebigen Coefficientenwerten den Ueberblick uber 
ihren Einfluss auf die dargestellte Grosse sehr erschwert und 
auch die Berechnung in manchen Beziehungen unbequem macht. 
Die Functionen R^ sind dagegen so gewahlt, dass der auf die 

73 



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74 A. SCHMIDT [Vol. I, No. 2 J 

ganze Kugelflache bezogene quadratische Mittelwert von^*cos;«A. 
und RZ sin m\ (hier mit Ausschluss des Falles m = o) bei alien 
derselbe (und zwar gleich i) ist. Auch ihre Maximal werte sind 
daher nicht sehr verschieden, z. B. 1.73 bei R l und R[, 3.32 bei 
R* t 2.33 bei R s s . In einer nach den RZ fortschreitenden Reihe 
ist demnach die Bedeutung jedes Reihengliedes dem absoluten 
Werte seines Coefficienten proportional, ein Umstand mit dem 
noch manche (zum Teil auch in der Eingangs erwahnten Unter- 
suchung hervortretende) Vorteile fur die Durchfiihrung der 
Zahlenrechnung verknupft sind. 

Um nun die Benutzung dieser Functionen zu erleichtern, 
gebe ich auf den folgenden Seiten eine kleine Tafel ihrer Loga- 
rithmen, die trotz ihrer weitgehenden Beschrankung fur die 
meisten Zwecke, besonders fur die Auswertung gegebener 
Reihen, ausreichen durfte. Eine Erweiterung und Vervollstan- 
digung der Tafel, insbesondere zur Erleichterung der Berech- 
nung der Reihencoefficienten, behalte ich mir fur spater vor. 

Es ist nicht meine Ansicht, dass man die Functionen R£ auch 
in den analytischen Entwickelungen stets gebrauchen solle ; in 
manchen Fallen wird es zweckmassig sein, diese in der bisher 
ublichen Form durchzufiihren und die RZ erst in die Schluss- 
ergebnisse einzusetzen. Um diese Umformung moglichst bequem 
zu gestalten, habe ich der Tafel die Logarithmen der Quotienten 
der verschiedenen Functionen hinzugeftigt. Es ist dabei 

gesetzt worden. Dazu ist noch zu bemerken, dass fur n = o, 
m = alle drei Functionen ubereinstimmend gleich 1 sind. 

Zur Berechnung der mitgeteilten Zahlen dienten siebenstel- 
lige Logarithmen, die in einigen Fallen bei der Abrundung auf 
fiinf Dezimalen eine Unsicherheit in der letzten Stelle bestehen 
liessen. Als moglicher Fehler der Zahlen ist daher nicht eine 
halbe, sondern eine ganze Einheit dieser Stelle anzusehen. 



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LOGARITHMEN DER KUGELFUNCTIONEN 



75 



u*.*J 



!<*.*; 



u*.*s 



i<*.*; 



log.*J 



0° 


0.23856 


— ao 


0.34949 


— 30 


— 00 


180' 


5 


0.23690 


9.17886 


0.34451 


9.52669 


8.16761 


175 


10 


0.23191 


9.47823 


0.32938 


9.82107 


8.76636 


170 


15 


0.22350 


9.65156 


0.30350 


9.98599 


911301 


165 


20 


0.21 155 


9.77261 


0.26569 


0.09508 


9.35512 


160 


25 


0.19584 


9.86451 


0.21405 


0.I7I27 


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7 6 



A. SCHMIDT 



[Vol. I, No. 2 J 



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ON THE EXISTENCE OF VERTICAL EARTH-AIR ELEC- 
TRIC CURRENTS IN THE UNITED KINGDOM/ 

By A. W. Rucker, M.A., F.R.S. 

In a paper by Dr. Adolph Schmidt, read before Section A of 
the British Association at Oxford {Report Brit. Assoc, 1894, p. 
570), the author stated that he had expanded the components of 
the Earth's magnetic force in series, and had deduced expres- 
sions, two of which give the magnetic potential on the surface 
of the Earth in so far as it depends on (1) internal, and (2) 
external forces. "The third series represents that part of the 
magnetic forces which cannot be expressed in terms of a poten- 
tial, but must be due to electric currents traversing the Earth's 
surface." The author concludes that such currents amount on 
the average to about 0.1 ampere per square kilometer. 

It appeared therefore desirable that this conclusion, drawn 
from the magnetic state of the Earth as a whole, should be tested 
by means of those portions which have been most fully studied. 

The test to be applied is, whether the line-integral of the 
magnetic force taken round a reentrant circuit on the surface of 
the Earth is or is not a vanishing quantity. 

The irregular form of the United Kingdom makes the appli- 
cation of this test more difficult than it would otherwise be ; but 
as two detailed surveys of Great Britain and Ireland have been 
carried out by Dr. Thorpe and myself for the epochs 1886 and 
1 89 1 respectively, the data at our disposal are so numerous that 
I thought it worth while to undertake the inquiry. 

The actual work of calculation has been carried out almost 
entirely by two of my students, Messrs. Kay and Whalley. My 
best thanks are due to them for the care and skill they have dis- 
played. 

The facts on which the investigation is based are as follows : 

'From the Philosophical Magazine for February 1896. Read before the Physical 
Society, December 13, 1895. 

77 




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7^ A. W. RUCKER [Vol. I. No. 2] 

The first survey (1886) included 205 stations, at all of which 
observations were made by Dr. Thorpe or myself. 

The true, and therefore irregular, isomagnetic curves were 
drawn for the epoch January 1, 1886, and the terrestrial curves \ 
from which the local disturbances were eliminated, were also 
calculated for the same date {Phil. Trans. Vol. CLXXXI, A, 
1890). 

The second survey included observations at 677 stations. 
These were made by ourselves, or, under our superintendence, 
by Messrs. Briscoe, Gray, and Watson. The results are about 
to be published by the Royal Society. The terrestrial isomag- 
netic curves were drawn for the epoch of January 1, 1891. The 
secular change having been carefully determined by special 
observations and methods, the values of the elements and the 
terrestrial curves obtained for the earlier date were reduced to 
January 1, 1891. Thus the whole of the 882 stations were avail- 
able for drawing the true isomagnetics for the latter date. The 
two sets of terrestrial curves obtained from the second survey 
and from the first survey reduced to the second epoch did not 
agree exactly, and the lines bisecting the intervals, between 
them were taken as our final result for the terrestrial curves in 
1891. 

The following sets of curves will be considered in this paper : 

( 1 ) The terrestrial isomagnetics obtained in the first survey 
for January 1, 1886. These will be referred to as the 1886 curves. 

(2) The same curves reduced by the secular change to Janu- 
ary 1, 1 89 1. These will be called the first survey 1891 curves. 

(3) The terrestrial curves for 1891 deduced from the second 
survey. These will be called the second survey 1 89 1 curves. 

(4) The mean terrestrial curves for January 1, 1891, deduced 
from (2) and (3). These will be called the mean 1891 curves. 

(5) Lastly, the true isomagnetic curves deduced from the 
results at all the 882 stations for the epoch January 1, 189 1. 
These will be called the true 1891 curves. 

(i) THE 1886 CURVES. 

The advantage of using the calculated terrestrial curves is that 
they can be carried across the sea from England to Ireland, or 



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VERTICAL EARTH AIR ELECTRIC CURRENTS 79 

extended a few miles from the coast by extrapolation. The 
area included can therefore be made as large as possible. On 
the other hand, the method of obtaining these curves is such that 
the errors in their positions will probably be greatest near the 
boundaries of the land area over which the survey was carried. 
In order therefore that such errors might affect different calcu- 
lations as differently as possible, it was determined to take two 
circuits, which should have their greatest extensions north and 
south, and east and west respectively. They will be called the 
a and P circuits. 

The a circuit was bounded by long. 2° W., lat. 58 N., long 
7 W. and lat. 52° N. 

The p circuit was bounded by long. i° W., lat. 55 N., long. 
9 W. and lat. 52 N. 

In the published account of the 1886 survey (loc. cit. p. 322) 
the values of the declination (8) and horizontal force (If) are 
given for all points within the United Kingdom defined by the 
intersection of whole degrees of latitude and longitude. From 
these the northerly components of the force (H cos 8) were 
calculated for all such points on the lines of latitude, and the 
westerly components (HsinS) for all such points on the lines 
of longitude which bounded the circuits. 

The method of calculating the line-integral of the force may 
best be shown by an example, for which we may select long. 2° 
W. between lat. 52 and 58°. 

Let Cbe the number of cm. in a degree of latitude, and N the 
northerly component of the force. Assume that N=N S2 + al' + x % 
where a is a constant, /'=/ — 52, and x is a small variable. 

Let W be the work done as the unit pole moves due north 
from lat. 52 to lat. 58°. 

Then W=C jj* Ndl^C j N„ X 6 + iSa +f*x<U' } • 

The value of a was found from the values of the northerly 
components at the points on latitudes 52 and 58 respectively. 
The integral was calculated by quadrature, graphic methods 
being employed. 

To give an idea of the relative magnitudes of the terms, I 
append the following data : 



80 A. W. RUCKER [Vol. I, No. 2) 

6 N<p + i8« + I .*///' = 1.00896 — 0.06864 — 0.00152 = 0.93880. 

The constant C was taken =111 19320 cm., so that the work 
done in this part of the circuit is 1.04387 X io 7 ergs. 

Treating the other parts of the circuit in the same way, the 
four quantities, the algebraical sum of which is the work done in 
completing the circuit, are : 

(1.04388+0. 1 7082 — 1.00637 — 0.20902) X io 7 = — 6.9X io 3 ergs. 

Dividing by 4*r, we find that the total current within the cir- 
cuit is — 550C.G.S. units, and, since the area is 2.13 X io 5 square 
kilometers, this amounts to — 0.026 ampere per square kilome- 
ter. The negative sign indicates that the current flows down- 
wards. 

A similar calculation carried out with respect to the & circuit 
of which the greatest extension is east and west and the area is 
1.77 X io 5 square kilometers, indicates a current of only — 0.004 
ampere per square kilometer. 

(2) THE FIRST SURVEY I89I CURVES. 

When the 1886 curves are reduced to the epoch January 1, 
1 89 1, by methods which are fully described in the account of 
the later survey, the results obtained from the a and P circuits 
are — 0.045 and — 0.030 ampere per square kilometer respec- 
tively. It would at first sight appear as though the fact that 
these values are larger than those calculated for January 1, 1886, 
might be due to errors introduced by the assumed values of the 
secular change ; but, as will immediately be seen, they are not 
larger than those obtained by another method, which this cause 
of error does not affect. 

(3) THE SECOND SURVEY I89I CURVES. 

Treated in exactly the same way as the last, these give val- 
ues of about the same magnitude but of opposite signs ; viz., for 
the a circuit + 0.046, and for the ft circuit + 0.020 ampere per 
square kilometer. Thus two different methods of calculating the 
same quantity lead to very different results, which point to the 
conclusion that the apparent effects of the hypothetical currents 



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VERTICAL EARTH* AIR ELECTRIC CURRENTS 8 1 

are due to small errors in the determination of the exact posi- 
tions of the lines. 

In the final calculation of the results of our survey, we have 
taken the means of the positions of these two sets of lines as the 
isomagnetic lines for 1891, hence the mean values of the currents 
deduced from them by the 

(4) MEAN I 89I CURVES 

are + 0.001 and — 0.005 ampere per square kilometer for the 
a and & circuits respectively. 

(5) THE TRUE 1 89 1 CURVES. 

We have further checked the above results by means of the 
true curves, taking two circuits — one (y) in England and Scot- 
land, and the other (8) in Ireland. 

The first of these was as follows : 

Long. i° E. from lat. 51 to lat. 53 . Lat. 53 from long. i° E. to i° W. 

Long. i° W. from lat. 53 to 55 . Lat. 55 from long. i° W. to 3 W. 

Long. 3 W. from lat. 55 to 53. Lat. 53 from long. 3 W. to 4° W. 

Long. 4 W. from lat. 53 to 51 . Lat. 51 ° from long. 4 W. to i° E. 

The area is 1.054 X io 5 square kilometers. The values of 
the horizontal force, and declination for every 10' of latitude or 
longitude were read off from the maps on which the values at 
the different stations were entered, and the true isomagnetics 
drawn. This operation was performed by Messrs. Kay and 
Whalley and checked by myself. The northerly or westerly 
component of the force was then calculated for each of these 
points, and the average value for each short section was assumed 
to be equal to the mean of the values at its initial and final 
points. 

No difficulty arose except at a point in Wales, where the 
curves are closed, and where it was therefore necessary to assume 
an average value for a section of the line on which a maximum 
occurred. 

The result of the calculation gave a current of — 0.008 ampere 
per square kilometer. 

The second circuit was taken in Ireland. It traversed the 
district of Antrim, in which there are violent local disturbances, 



Digits 



82 A. W. RUCKER 



[Vol. I, No. 2] 



and is interesting chiefly as showing to what extent the result 
may be affected by such causes. 
The circuit was as follows : 

Long. 6° 30' W. from lat. 52 to lat. 55 . 

Lat. 55 from long. 6° 30' to long. 8°. 

Long. 8° from lat. 55 to 54 . 

Lat. 54 from long. 8° to 9 . 

Long. 9 from lat. 54 ° to lat. 52°. 

Lat. 52 from long. 9 to long. 6° 30' W. 

The area is 48 X 10 3 square kilometers. 

The current is — 0.046 ampere per square kilometer. 

The fact that these different circuits, including areas of very 
different magnitudes and situated in different parts of the United 
Kingdom, all give very small values for the hypothetical currents, 
is strong evidence that the smallness of the calculated numbers is 
not due to the fact that large positive and negative values mutu- 
ally cancel each other. It is, for instance, conceivable that the 
directions of the current-flow might be opposed on what may be 
called the oceanic and continental sides of the kingdom. 

If this were so, it is probable that circuits y and 8 would have 
given results of opposite signs. By way of testing the matter 
further, the current was calculated both from the 1886 and the 
1 89 1 lines for the relatively small area in the west of Ireland 
bounded by latitudes 52 and 53 , and longitudes 9 and io°. 

The results were : 

For 1886, — 0.04 ampere per square kilometer. 
For 1 89 1, + 0.11 ampere per square kilometer. 

Hence the difference of direction which characterized the 
currents deduced from the two surveys when applied to large 
areas, also distinguishes, and in an exaggerated degree, the 
results obtained from a small border district. It is therefore 
evident that either the distribution of the vertical currents has 
entirely altered in five years, or they are too small to be detected 
by the method employed. 

The former of these hypotheses is negatived by the fact that 
different calculations, based on the first and second survey 1 891 
curves respectively, lead to discordant results for the same date, 



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VERTICAL EARTH -AIR ELECTRIC CURRENTS 83 

and we are therefore compelled to fall back upon the second 
alternative. 

EFFECT OF THE ELLIPTICITY OF THE EARTH. 

The question may fairly be raised whether, in dealing with 
such minute quantities, the ellipticity of the earth ought not to 
be taken into account. 

In answer to this, it may be stated that the work done when 
the unit pole traverses the a circuit was also calculated, using 
the data as to the form of the Earth given by Captain Clarke and 
quoted by Professor Everett (C.G.S. System of Units, ed. 1891, p. 
71). The numerical values thus obtained differed from those 
given above, but the differences between them were of the same 
order. Both methods of calculation lead to opposite conclusions 
as to the directions of the hypothetical currents according as the 
1886 or 1891 curves are used; thus proving that the small out- 
standing uncertainties as to the magnetic state of the United 
Kingdom are the cause of the discrepancies, which are not 
reduced by using a closer approximation to the form of the 
Earth. 

CONCLUSION. 

I can only conclude from these various figures that the local 
magnetic surveys furnish no evidence of vertical electrical cur- 
rents in the United Kingdom. The largest number obtained 
from the larger circuits is less than half that which Dr. Schmidt 
assigns as the mean value for the whole Earth. Different calcu- 
lations lead to results of different signs for the same quantity ; 
and the data which would a priori be accepted as the best give 
the smallest values. 

As far as the terrestrial curves are concerned, the final results 
for the two surveys are embodied in the 1886 and the mean 1891 
curves respectively. The local irregularities in the north of 
Ireland are so great that the calculations based on the true iso- 
magnetics in that country may be neglected as compared with 
the probably much better results obtained in Great Britain. 

Selecting, then, only the most trustworthy values, the results 
may be summed up as follows in terms of amperes per square 
kilometer: 



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8 4 A. W. RUCKER [Vol. I. No. 2] 

Circuit 

« P y 

1 886 — O.026 — O.OO4 
1 89 1 +O.OOI — 0.005 
1 89I — O.OO8 

From these figures we may conclude that there is not in the 
United Kingdom a vertical current amounting on the average to 
O.i ampere per square kilometer. They are not inconsistent with 
the existence of a current of about a tenth or a twentieth of that 
amount ; but on account both of the smallness of the results and 
of the discrepancy between the values obtained for 1891 by two 
methods, we cannot assert that such a current actually exists. 
The calculations taken by themselves do not disprove the 
hypothesis that electric currents traverse the Earth's surface, as 
we cannot argue from the condition of a small portion of the 
globe to that of the whole. The most that can be said is that 
no evidence in favor of the existence of vertical currents can be 
drawn from one district, which has been very minutely surveyed. 

P. S. — No reference to Dr. Schmidt's original paper was 
given in the short notice published in the report of the British 
Association. I had therefore supposed that the latter was a pre- 
liminary note. Professor Schuster has, however, recently shown 
to me Dr. Schmidt's complete investigation, and he has kindly 
calculated the current-density at latitudes 50 and 55 on the 
prime meridian from formulae given by Dr. Schmidt. The result 
is upward currents and 0.20 to 0.15 ampere per square kilometer 
at latitudes 50 and 55 respectively. The mean of these two 
numbers, viz., 0.175, is nearly equal to Schmidt's mean for the 
whole Earth (0.17). It is opposite in direction to and very 
much greater in magnitude than any vertical current the exist- 
ence of which is compatible with the results of the Magnetic 
Survey. 



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LETTERS TO EDITOR 



MAGNETIC DECLINATIONS OBSERVED NEAR THE SPITZ- 
BERGEN ISLANDS IN 1894.— A Report. 1 

During the summer of 1894, while acting as astronomer for the 
Wellman Polar Expedition, I succeeded in making a few observations 
to determine the declination of the magnetic needle in the region of 
the Spitzbergen Islands, the results of which, I enclose herewith for 
use in any way you may wish, and hoping they will be of some little 
value to anyone interested in the subject. 

Magnetic Declinations near the Spitzbergen Islands. 

N * Date, Hour Latitude L °gS? de TWH„..u>n 

£ Civil Local M.T. North Gr ^J ich DeeHwi- 

h m 

1 May 10 6 00 p.m. 79 40' io° 35' E. 17* 28' W. 

2 May 18 7 30 p.m. 80 38 19 42 E. 9 38 W. 

3 June 8 11 00 a.m. 80 32 23 10 E. 5 35 W. 

4 June 19 II 30 a.m. 80 26.1 23 18 E. 5 17 W. 

4 June 19 I 15 p.m. 80 26.1 23 18 E. 5 54 W. 

5 June 24 9 00 a.m. 80 25.7 24 16 E. 4 49 W. 
5 June 24 1 30 p.m. 80 25.7 24 16 E. 5 33 W. 

Description of Stations. 

1. The instrument was mounted on the rocks just east of the house 
belonging to Mr. Pike on Dane's Island, one of the small islands on 
the northwest side of the Spitzbergen group. 

2. Instrument was set on the ice near the north point of Walden 
Island, not more than 150 feet from the rocks of the island. Walden 
Island is the most southwestern of the Seven Islands, the group just 
north of Spitzbergen Islands. 

3. Instrument was mounted on the ice about a half a mile north of 
Cape Platen. 

4. This station was located on the first prominent point east of 
Cape Platen and distant about four miles therefrom. 

5. This station was on the extreme north point of the Inner Rep 
Island, Outer Rep being about two miles to the northward. 

'This report was made at my request for communication to the Journal — C. A. 
Schott, U. S. Coast and Geodetic Survey. 

85 



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86 O. B. FRENCH [Vol. I, No. 2] 

Instruments Used. 

For the determination of the latitude, local time and azimuth a small 
four-inch, Casella theodolite was used. It was mounted on a tripod and 
fairly stable and steady. Both the circles were graduated to half 
degrees and read by two verniers to minutes. 

For the determination of the declination of the magnetic needle, a 
compass declinometer was used being mounted on the tripod, in place 
of the theodolite, for the purpose. This compass declinometer is 
somewhat similar to a prismatic compass having a graduated circle 
about five inches in diameter reading by two pointers to minutes. A 
reversible needle about three inches long is enclosed in a glass covered 
box. The prism for pointing on the needle end, the vertical thread 
for pointing on a distant mark, and the pointers for reading the circle 
are all attached to a movable plate for use in any direction. 

Difference in longitude was obtained by means of several watches 
carried by different members of the expedition. Only two however 
were utilized in the computations, as they showed rates very similar; 
during the four months between comparisons with Greenwich time, 
one lost about twenty seconds, the other forty seconds. 

Character of the Observations. 

All observations for position were made on the Sun's center, the 
diaphragm of the telescope having a square cut on it so that the corners 
just touched the circumference of the Sun. The usual method of pro- 
ceeding was to take readings on a mark with telescope, both direct and 
reversed, and then two pointings on the Sun noting the time and reading 
both circles each time, then reverse telescope and take two more pointings 
and readings thus making a "set." This was followed immediately by 
another set, then the theodolite was dismounted and compass declinome- 
ter put in its place. A set of observations for declination consisted in 
two pointings on the mark reading both pointers, then two pointings 
on each end of the needle reading both pointers ; then after removing 
top of box, inverting needle, and replacing top so that circle is reversed 
repeating the observations already made. 

At stations one and two the determination of the latitude is very 
weak as the Sun was very near the prime vertical. At Dane's Island 
only one set was observed and hence the latitude may be in error 8' or 
10'. Longitude and azimuth are very fair however. 

At stations four and five the latitudes were obtained from circum- 
meridian altitudes and are very good, seven determinations at No. 4 
having a range of only 1 ' and six at No. 5, only o'.8 range. The two 



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LETTERS TO EDITOR 87 

results for azimuth at each of these stations differ by only a half 

minute, the longitudes being correspondingly good. 

The observations for declination were made at irregular periods of 

the day. As no observations were made to determine the diurnal 

range they could not be reduced to mean of day. It was the intention 

of the observer to make a complete set of observations hourly during 

the whole twenty-four hours on several days but numerous other duties 

prevented. Owen B. French, 

_ Aid, U. S Coast and Geodetic Survey. 

Washington, D. C, 

Nov. 29, 1895. 



OLD MAGNETIC DECLINATIONS. 
Mr. Schott writes : " I have before me a work which contains a collection 
of magnetic declinations in parts of Europe, America, Asia and Islands, pub- 
lished originally at Amsterdam in 1 599. The title of the book is ' Clavdii 
Aeliani Tactica sive etc.' Lugdvni Batavomm Apud Ludovicum Elzevirium, 
anno CIDIDCXIII [16 13]. This is a treatise on ancient warfare. Our 
special interest centers in the second part of the book with the sub-title : 
'AIMENETPETIKH sive Portunus investigandorvm ratio;* by Hugo Grotius 
(de Groot). In the table latitudes and longitudes are given along with the 
declination but no clue to the dates can be obtained except that they must 
pre-date 1599. As it contains no place on our coast I have paid no further 
attention to it." 

Van Bemmeleris search for old magnetic declinations. High praise must 
be accorded Dr. van Bemmelen for his most painstaking and fruitful labors 
in this direction. Only one who has been engaged in a similar task can fully 
appreciate the amount of true patience and skill needed. It is a labor of love 
for which every magnetician owes Dr. van Bemmelen a large debt of grati- 
tude. Since writing the letter which appeared in the first number of the 
Journal, he informs us that during a trip to London he has found additional 
valuable material. He hopes soon to be able to present the readers of the 
Journal with an improved series of isogonic maps of the sixteenth and sev- 
enteenth centuries. 

There are doubtless many others in a position to contribute valuable data 
were they to follow his example. Such researches are absolutely essential if 
we wish to make continued progress in the study of the secular variation and 
the distribution of terrestrial magnetism. Too many have the false impres- 
sion that an old observation with a probable error of a degree or of several 
degrees is absolutely worthless, whereas, really the probable error is often but 
a small fraction of the total secular variation during the time interval consid- 
ered. Likewise a large systematic error running through a series of observa- 
tions does not affect the relative distribution. We trust that those engaged in 
similar researches will put themselves in communication with Dr. van Bem- 
melen, assistant director of the Royal Meteorological Institute of the Nether- 
lands, Utrecht. 



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88 Af. ESCHENHAGEN [Vol. 1. No. 2] 

UEBER DIE FRAGE, IN WELCHER FORM DIE MAGNE- 
TISCHEN OBSERVATORIEN IHRE ERGEBNISSE 
VEROFFENTLICHEN SOLLEN. 

Es ist sicher die Frage von Wichtigkeit, in welcher Form die mag- 
netischen Observatorien ihre Ergebnisse veroffentlichen sollen, ob 
man Polarcoordinaten oder rechtwinklige Coordinaten zur Darstellung 
der Variationen der erdmagnetischen Kraft wahlen soil ; wichtiger 
aber erscheint mir die Vorfrage, in welchem Umfange sollen die unmit- 
telbaren Beobachtungsergebnisse in den Jahrbuchern veroffentlicht 
werden. Gewiss ist es hdchst niitzlich fiir einen Bearbeiter, gleich die 
tagliche Periode z. B. der rechtwinkligen Componenten, dargestellt 
durch 24 Stundenwerthe oder noch besser durch die Coefficienten der 
trigonometrischen Reihen, gedruckt zu finden, aber zunachst ist doch 
die Frage zu losen, welches Material soil diesen Ableitungen zu Grunde 
gelegt werden. Sollen ungestorte Tage ausgewahlt werden, so miissten 
dieselben fiir alle Observatorien dicsclben sein. sie miissten also nach vor- 
herigem Einverstandniss ausgesucht werden. AUein wiirden nur diese 
Tage publicirt, so wiirden Untersuchungen nach andernen Richtungen 
unmoglich gemacht werden. Meine Forderung geht also dahin: es sind 
zunachst von den Observatorien a lie, den registrirten Curven entnom- 
menen Stundenwerthe jedes Tages in absolutem Maass nebst dem tdglichen 
Gang fur den Monat zu publiciren und zwar in der Form, in 
welcher die Componenten beobachtet werden, als Declination, Hori- 
zontal-Intensitat und Vertical-Intensitat. Alle weiteren Rechnungs- 
resultate, die selbstverstandlich erwunscht, aber doch nicht unbedingt 
nothweiidig sind, da sie immer noch aus dem gegebenen Material 
gewonnen werden konnen. Nicht aber kann z. B. der tagliche Gang 
fur alle Tage gefunden werden, wenn man nur die ungestorten 
veroffentlicht hat. 

Ferner aber scheint mir ausserordentlich wichtig, dass aus einer 
Publication zu ersehen is, in wie weit sind die Scaienwerthe sicher, und 
wie ist die Ableitung der Werthe fur Scalentheil aus den absoluten 
Messungen geschehen, die Schwankungen dieses Werthes miissen mit- 
getheilt werden. Ferner wie gross ist die Sicherheit der absoluten Mes- 
sungen, endlich wie gross ist der Temperatureinfluss auf die Variations- 
Instrumente und wie weit ist der tagliche (Jang von demselben befreit. 

Diese Fragen, die von mir bereits auf der Miinchener Conferenz 
(189 1) angeregt sind, sind meines Erachtens zuerst zu losen, und esware 
ein grosser Gewinn, wenn ein Meinungsaustaush hieruber zu einem 
gunstigen Resultate fiihrte. M. Eschenhagen. 

Potsdam, 7. Februar 1896. 



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LETTERS TO EDITOR 



89 



SOME SECULAR VARIATION EXPRESSIONS OF THE MAGNETIC 

DECLINATION.' 



Station 


Lat. 


Long 
from G 


r. 


Empirical Expression 
D= 


Epoch 




1 


12 47 


N 


44 59 


E 


9 .20 - 5 .S9Xsin(i»i r-f 224 .0) 


1612-1887 


±43 -o 


44O 


1, Peru 


18 28 


S 


70 20.5 YV 


— 9 .40 — I .46 


sin(i .57- i- 278 .8) 


I7I3-I893 


06 .0 


240 


nsion Id. 


7 55-5 


s 


14 24 


\V 


10 .55 - 13 .45 


sin(o ,6r-r- 45 .3) 


1 700- I 890 


22 .61600 


iland. N. Z. 


36 50 


s 


174 49 


E 


-14 .36 - .46 


sin(i .1 t+ 30 .6) 


1 848- 1 89 1 


10 .OJ327 


ua, Java 


6 08 


s 


106 48 


E 


I .50 -*■ 3 .16 


sin(o .gr t 247 .8) 


1605-1885 


15 .0 


400 


bay 


18 56 


N 


72 54 


E 


2 .66 -r 3 .49 


sin(o .8T-+-242 .2) 


1722-1889 


12 .0 


45C 


gctown 


13 05 


N 


59 37 


YV 


- I .54 - 2 .74 


sin(i .2r+ 17 .2) 


1726-1893 


15 .0 


300 


tos Avres 


34 36 


S 


58 22 


YV 


-12 .03 -t- 3 -50 


sin(i .or4-io .05) 


1 829- 1 883 


38 .0 


360 


agena 


10 25 


N 


75 32 


YV 


- 5 .81 r 2 .08 


sin(i .2t+ 22 .5) 


1705-1888 


15 .8 


300 


? of Good Hope 


3>3 56 


S 


18 29 


E 


14 .63 -r-15 .00 


sin(o .61 t | 77 .8) 


1605-1890 


22 .5 


590 


lottetown, Pr. Kd. Id. 


46 14 


N 


63 08 


YV 


15 -15 + 7 .96 


sin(18 T-r- 77 .6) 


1 842- 1 886 


20 .0 


380 


of Mexico 


19 26 


N 


99 05 


YV 


-5-52 + 3 -09 


sin(i .OT+270 .5) 


1760-1885 


18 .0 


360 


:tpcion 


36 42 


S 


73 07 


YV 


-13 .63 -r 3 -52 


sin(i .OT-j-256 .6) 


1 709- 1 893 


23 .2 


360 


aimbo 


29 57 


S 


71 22 


YV 


-11 .55 + 2 .83 


sin(i .OT-l-264 .3) 


1700-1891 


21 .0 


360 


icao 


12 07 


N 


68 57 


YV 


— 4 .91 + 2 .82 


sin(i .or+ 23 .1) 


1 704- 1 894 


13 7 


360 


il T Azores 


38 32 


N 


28 33 


YV 


11 .82 +14 .75- 


sin(f| t+ 89 .1) 


1 590- 1 89 1 


46 .0 


530 


de France 


U 36 


N 


61 04 


YV 


- 2 73 + 3 .30 


sin(|f T-i- 27 .6) 


1682-1887 


19 .0 


330 


tpagos Is. 


1 00 


S 


90 00 


YV 


- 7 .49 -t- 1 .91 


sin(i .St + 272 .1) 


1794-1880 


25 .0 


240 


ifax, Nova Scotia 


44 39-6 Nj 63 353 W 


16 74 | 4 .30 


sin(|5 t+ 39 .5) 


1700-1879 


26 .0 


35o 


►ana 


->3 09 


N. 82 22 


YV 


-3-42 + 3 -M 


sin(i .or— 318 75) 


1726-1889 


17 .0 


360 


jua\ ra 


10 36 


N 


66 56.5 YV 


- 3 .58 + 1 .61 


sin(i .0H-357 7) 


1 800- 1 890 


21 .0 


360 


rwin Head, Mexico 


28 15 


N 


114 06 


YV 


— 9 .85 — 1 .99 


sin ( \° t +229 7 < 


1783-1888 


09 


252 


jdalena Bar- 


24 38 


N 


112 07 


YV 


- 7 .48 + 3 ." 


sin(\° t +241 .8) 


1783-1881 


35 .0 


252 


illa, Luzon Id. 


"4 36 


N 


120 58 


E 


— .22 + .58 


sin(i .ot -f 226 .3) 


1 7 66- 1 890 


08 .3 


360 


Ac video 


34 54 


S 


56 12 


YV 


— 10 .28 -r- 3 -90 


sin(i .OT-i-358 .3) 


1 790- 1 894 


12 .3 


360 


asaki 


32 43 


N 


129 51 


E 


2 74 - 1 .0237 (t) ^0.0000774 ( T )* 


1 805-1892 


05 .1 





yV6 


23 39 


S 


43 36 


E 


15 -31 -♦- 8 .30 


sin(o .6x^146 .1) 


J 607- 1 890 


30 .0 


600 


una 


8 57 


N 


79 32 


YV 


— 6 .54 + 1 .37 


sind ,8t— 4 .4) 


1776-1885 


13 -c 


200 


ta, Peru 


5 05 


S 


81 05.5 


YV 


— 7 .42 + 1 76 


sin(i ,2T-t 288 .4) 


1821-1894 


14 .2 


300 


in 


39 54 


N 


116 28 


E 


2 .179+ .013 


1 (t) -0 .oooii7(t)» 


1755-1887 


06 .0 





lambuco 


8 03 


S 


34 52 


YV 


8 .99 - 9 .46 


sin(o .9^4-356 7) 


1815-1894 


17 .4 


400 


tjpaulowski 


53 01 


N 


158 43 


E 


- 2 .68 + 3 .35 


sin( l 7 ° r+ .3) 


1779-1891 


21 -3 


252 


a and Guayaquil 


a is 

S 18 


S 


79 52 


YV 


— 8 .46 -f- .02 


r)+o .0001 (t)».. . 


1791-1880 


10 .0 


— 


la Arenas 


53 10 


s 


70 54 


YV 


— 18 .68 + 5 .12 


sin(l .OT+301 .9) 


1766-1893 


16 .6 


360 


de Janeiro 


22 54 


s 


43 10 


YV 


1 .81 4- 8 .86 


sin(l .or-f 348 .1) 


1768-1888 


25 .0 


360 


tahns, N. F. 


47 34 


N 


52 41 


YV 


15 -63 +15 .52 


sin(i .ot-(- 72 .0) 


1845-1885 


17 -4 


360 


Bias, Mexico 


21 32 


N 


105 19 


YV 


— 6 .60 + 2 .82 


sin(V> T+258 .6) 


1 783-1 880 


26 .0 


252 


Helena 


15 55 


S 


5 44 


YV 


7 .90 -f-15 .92 


sin(o .6t+ 68 .2) 


£610-1890 


41 .8 


600 


Vincent 


16 53 


N 


24 59 


YV 


10 .48 -Ho .22 


sin(o .6t+ 45 .2) 


161 5-1 894 


25 .0 


600 


Diego, Cal. 


32 43 


N 


117 70.3 W 


—11 .85 - 1 .33 


sin(i .5T+214 .6) 


1783-1889 


11 .0 


24O 


japore 


1 18 


N 


103 51 


E 


.24 -f 2 70 


sin(o .9T-J-244 .1) 


1824-1891 


17 .0 


400 


ibaya. Java 


7 H 


S 


112 45 


E 


2 74 + 4 70 


sin(o .9x^234 .6) 


1793-1876 


06 .4 


40C 


liti, Society Id. 


17 3i 


S 


149 34 


YV 


— 5 .64 4- 1 -95 


sin(i .OT-l-244 .9) 


1768-1878 


14 .0 


360 


a Cruz 


19 12 


N 


96 08 


YV 


— 4 -77 + 3 .91 


sin(i .ot4 279 .0) 


1726-1889 


dz 29 .0 


360 



Washington, D. C. 



G. YV. LITTLEHALES. 



'For details, I beg to refer to the Hydrographic Office Publication, No. 109a, Contributions to Terrestrial 
znetismi the Variation of the Compass. West declination is ft/us, east declination, minus ; t stands for date — 
0. Special care has been taken in the preparation of the above table. YY'here discrepancies occur between 
data contained therein and those on pages 50 and 52, *' Publication 1 09^7," the data given here should be 
Mi. The expression for Bahia, Brazil, it was thought better to omit. 



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NOTES 

We welcome among the "Associates" Professors Mascart and Neumqyer, 
whose names were received too late to be inserted in the first number. The 
Journal is assured of their heartiest cooperation and good will. 

Among the contributors in future numbers will be Messrs. Abbe, van 
Bemmelen, Biese, BSrgen, Eschenhagen, Lemstrdm, Ltideling, Mendenhall, 
Moureaux, Neumayer, Riicker, Schaper, Schuster, Schmidt, Schott, and 
Weinstein. 

M. Moureaux has been entrusted by the Minister of Public Instruction, at 
the request of the Imperial Russian Geographical Society, with the investiga- 
tion of a pronounced "anomaly" in the distribution of terrestrial magnetism, 
which certain observations have revealed in southern Russia. He will, in 
consequence, be prevented from contributing his promised article on self- 
registering magnetic instruments, which was to have been written at Mascart's 
suggestion, for the July number of the Journal. 

Mr. William Ellis, F.R.S., formerly Superintendent of the Magnetic 
and Meteorological Observatory, Greenwich, now retired, who has eclipsed 
the record of long service at Greenwich — having served a full half century — 
writes us that he is in thorough sympathy with the aims and purposes of 
the Journal. " Terrestrial Magnetism," he says, " has been a greatly 
neglected science, there is hence great need for some such definite place for 
contributions as this Journal." He will do what he can for it. May we hear 
as favorably from all co-workers! 

What is thought of " Terrestrial Magnetism" — The whole number, includ- 
ing the chart, is very nicely got up." — C. Chree. " Ich gratulire zur ersten 
Nummer. Sehr gelungen!" — G. Hellmann. "I am much pleased with the 
appearance of the first number of Terrestrial Magnetism, and I think the 
contents are of such interest and promise as to do much towards making the 
future of the Journal successful." — T. C. Mendenhall. " Die erste Nummer 
von Terrestrial Magnetism habe ich heute erhalten. Die Ausstattung ist 
brilliant und der Inhalt von grosser Bedeutung. Die EinfUhrung des Journals 
lasst demnach nichts zu wiinschen Ubrig." — C. Borgen. "Die erste stattliche 
Nummer der Zeitschrift gefallt uns alien sehr, endlich der Beginn von dem 
lang ersehnten Fortschritt ! Ich verspreche mir viel davon, da ein Zusammen- 
arbeiten moglichst vorbereitet wird." — M. Eschenhagen. " Soeben erhalte ich 
das erste Heft von Terrestrial Magnetism. Ich finde, dass es einen sehr 

90 



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NOTES 9 1 

gut en Eindruck macht und begluckwlinsche Sie von Herzen." — Ad. Schmidt. 
•• Vol. I., No. i, just received, and it makes a very handsome appearance, 
quite as creditable to the University as it is to yourself." — C.Abbe. Professor 
JVeumayer congratulates upon the success achieved "by starting such a 
valuable publication." 

Special thanks are due M. Lancaster for the great pains he has taken to 
bring the Journal to the notice of the readers of del et Terre. After giving 
a complete translation of the circular of announcement, he says : " Ciel et 
Terre se chargera bien volontiers d'envoyer les souscriptions a destination." 
. . . " Nous souhaitons a la nouvelle revue le plus, grand succes, et la 
realisation du but qu'elle se propose de poursuivre." 

A few of the press notices are also appended : 

"The magnetic needle has become such a promising instrument of 
research, not only in terrestrial, but in cosmical physics, that the journal 
which is to be devoted to phenomena connected with it will appeal to a large 
class of investigators." — Nature. 

41 We have adopted the unusual practice of setting out in full the title-page 
of the new journal, because the title-page is itself as unprecedented as is the 
publication ; never before was such a galaxy of names on the title-page of 
any periodical, never was the word ' international ' more fully deserved. We 
may further remark that such a journal was very much wanted, and that in 
the interest of scientific progress we sincerely hope that it may have a long 
and prosperous career. — Symons's Monthly Meteorological Magazine. 

The Geologist's Interest in Terrestrial Magnetism. Professor T. C. Cham- 
berlin, director of the Geological department of the University of Chicago, in 
the January- February number of Journal of Geology \ says : 

•' Geologists who are interested in the more obscure problems of the physics 
of the earth will welcome with peculiar gratification the appearance of a 
monographic periodical devoted to one of the most neglected phases of the 
earth's phenomenon, * Terrestrial Magnetism.' . . . . " The magazine 
will perform a valuable service in bringing together matter which is now so 
widely scattered as to be difficult of access even to specialists, and quite 
beyond the reach of most geologists. Without doubt it will also greatly pro- 
mote the organization of the matter and the evolution of the science. Not a 
few geologists have looked with some measure of hope to terrestrial magne- 
tism for a valuable contribution to the dark problems of the earth's interior. 
We have long felt that there should be discoverable some medium which 
could be operated upon by some inventible device in such a way as to serve 
as a stethoscope, so to speak, to declare the conditions and the changes in the 
heart of the earth. Magnetism is one of the suggested media, and, even if it 
shall not prove an agency of any great moment in itself, it may reveal condi- 
tions of the interior now quite hidden from us. The editorial greeting perti- 
nently quotes Maxwell's eloquent words — referring to the sensitized sheet of 
the self-registering magnetograph — • On that paper, the never resting heart of 
the earth is now tracing in telegraphic symbols, which will one day be inter- 
preted, a record of its pulsations and its flutterings, as well as of that slow but 
mighty working [the secular variation] which warns us that we must not sup- 
pose that the inner history of our planet is ended.' 

" The first number of the journal contains several articles of weighty inter- 
est to geologists." 



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92 NOTES [vol. I, No. 2] 

The National Geographic Magazine for February says : " The true 
cause of the behavior of a compass needle has been a field for speculation 
and study ever since its peculiar behavior was observed and a few students 
had up to the time of Gauss proposed and laboriously worked out ingenious 
theories to explain the phenomena observed. The publication of Gauss' 
great work in 1838, however, marked a great advance and gave a new and 
powerful impulse to the subject. The Magnetic Union, formed in the third 
decade of the present century, chiefly owing to the researches of Gauss, 
caused the establishment in various parts of the world of magnetic observa- 
tories, founded and maintained by various governments. Of those so founded 
in the forties, several have maintained a series of almost uninterrupted 
observations to this day. This period of sixty years has seen progress in our 
knowledge of terrestrial magnetism, but without any epoch-making event. 
A vast number of observations have been accumulated, the twenty-four con- 
stants in Gauss' fundamental formula have been more accurately determined, 
and a number of minor phenomena observed and explained, but the subject is 
far from being exhausted. The modern applications of electricity to practical 
affairs is not without its effect upon the subject of terrestrial magnetism. 

" Is not the Journal before us, then, to mark a new epoch in our knowl- 
edge of this subject? It seems strange that, when almost every other branch 
of science has long had its special journal or organ, we should have waited 
almost for the dawn of the twentieth century for the first number of the first 
journal devoted to a matter of such great practical moment and for four cen- 
turies known by all civilized men to be important. 

"We welcome this Journal, then, as a needed one, rightly conceived 
and giving promise of usefulness. It enters, and enters under favorable 
auspices, a field not hitherto occupied by any scientific journal. The names 
of the editors, the laboratory, and university from which it comes all combine 
to promise excellent results. It will be strange indeed if distinct gains in 
human knowledge do not result from this enterprise." 

The financial side of the Journal, Now that the scientific success of the 
Journal seems to be assured in that the united and harmonious support of 
magneticians the world over has been gained, strenuous efforts should be 
made to make the Journal self-supporting. Thanks to several liberal sub- 
scriptions received from "Associates" — one of them, an American, who will 
not permit the mention of his name, has made himself responsible for 25 sub- 
scriptions ($50) the first year — the Journal is on a better footing than the 
average new journal after the issue of its first number. Nevertheless, at 
least 50-75 new subscriptions are needed to cover the probable total outlay 
for the year. The Journal is not subsidized by any university or corpora- 
tion ; it will depend for its support upon those who have the advancement of 
Terrestrial Magnetism at heart. The editor does not intend that the Journal 
shall be conducted very long on a losing basis, — not that it is to be abandoned 
in case there is a deficit at the end of the year, but that the garment will 
be cut according to the cloth. A journal of Terrestrial Magnetism in some 
form or other has come to stay. 

New Magnetic Observatories. According to information received from 
the Director of the Meteorological Institute of Roumania, S. C. /fepiles, their 
Magnetic Observatory is now completed and ready for the installation of the 



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NOTES 93 

self-registering instruments. A magnetic survey of Roumania is to be under- 
taken ; a Wild transportable magnetic theodolite constructed by Edelmann 
and compared by Wild with the absolute instruments at the Pawlowsk Obser- 
vatory, has been secured. Dr. M. Snellen also writes us that the new Mag- 
netic Observatory at Utrecht, which we had the privilege of visiting during its 
construction, and which is more favorably located than the old one, is ready 
for the placing of the instruments. Descriptions of these observatories will 
be given later. Professor Neumayer promises an abstract of an interesting 
investigation that he is carrying on which will serve to point out where Mag- 
netic Observatories are most needed and where they can be established to 
best advantage. It is very much to be hoped that we may soon report the 
establishment of a permanent Magnetic Observatory at Chicago. May the 
day be not far distant when the United States of America will be able to 
make as good a showing of Magnetic Observatories as any of the European 
countries ! 

The Construction of new magnetic charts of the Earth by the French 
Bureau of Longitudes. 

M. de Bernardieres 1 has contributed a most interesting note to the Comptes 
Rendus, 121, p. 679, on the above subject. The spirited enterprise of which 
this note gives the first published account is another indication of the remark- 
able interest that is being displayed at the present time on all sides in 
geomagnetism. After briefly noting this reawakening interest the author 
gives a short description of the methods and purposes of the project. The 
object is to undertake under the direction of the Bureau des Longitudes 
the construction of new magnetic charts of the Earth, supplementing the data 
furnished by magnetic surveys and observatories by freshly observed material in 
such localities (at sea, along seacoasts, etc.,) where observations for various 
reasons are more or less defective or are entirely wanting. These observations 
are to be made in various parts of the Earth as nearly simultaneously as pos- 
sible by experienced or previously trained observers, all precautions being 
taken to secure strict comparability. 

The bureau has obtained the hearty co5peration of Vice- Admiral Bernard, 
Minister of Marine, who has put at its disposal officers, sailors, and a large 
number of instruments, also that of the Colonial Minister who has promised 
his active interest in the colonies. In this way it was made possible to organ- 
ize seven expeditions, each composed of a lieutenant, ensign or hydrographer, 
and one assistant. These expeditions have been distributed as follows : 

Atlantic Ocean. — West coast of Africa, east coast of America, Antilles, etc., 
M. Schwerer, lieutenant of the ship. 

Pacific Ocean. — West coast of America, M. Blot, ensign of the ship. 

Pacific Ocean. — Oceania, M. Monaque, ensign of the ship. 

Indian Ocean. — Red Sea, south coast of Asia, eastern coast of Africa, 
Madagascar and other islands, M. Paqu6, ensign of the ship. 

1 Secretaire de la Commission des Cartes magne*tiques du Bureau des Longitudes. 



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94 XOTES [Vol. I. No. 2j 

Chinese and Japanese Seas. — Coasts of Indo-China, of China and Japan, 
M. Terrier, ensign of the ship. 

Madeira, Canary Islands, Azores, Cape Verde Islands, Senegambia, M. 
de Vanssay, hydrographic sub-engineer. 

Iceland. — North Sea, Scandinavia, Denmark, Scotland, M. Houette, cap- 
tain of the frigate and in command of the station at Iceland ; M. Morache 
lieutenant of the ship. 

As soon as the necessary instruments are forthcoming an eighth expedition 
will be sent to Terranova, which on its return will make observations in the 
Mediterranean Sea. 

The observers are provided with both absolute and variation instruments. 
Instrumental tests and comparisons have been made before starting at the 
observatories of Montsouris and Pare Saint Maur. Observations and com- 
parisons will also be made at all the Magnetic Observatories en route. Full 
and definite instructions accompany each expedition, so that uniformity of 
method of observation and reduction may be secured. The Marine Depart- 
ment has promised to provide certain ships with the instruments necessary for 
accurate observations at sea. 

Six of the expeditions are en route ; they have already communicated their 
first observations. It is expected that they will carry on their work for about 
two years. 

The expedition sent on the ship "Manche" to Iceland last spring has 
returned with a large number of observations made at Cherbourg, in Scotland, 
the Shetland Islands, Iceland, Norway (as far north as Bossekop and Ham- 
merfest), in Denmark and in the North Sea. Two complete series of observa- 
tions of variations, each eight days in duration, were obtained by the Observa- 
tory constructed by the " Manche " at Reykiavik. An interesting and valua- 
ble comparison will thus be afforded with the observations of the " Recherche" 
obtained sixty years ago and with those of various other expeditions in these 
regions. It is hoped that the remainder of the expeditions will be equally 
successful. 

Abstracts of papers. In order to give prompt notice of current papers on 
terrestrial magnetism and allied subjects, we would be greatly obliged if 
authors who have articles appearing elsewhere will kindly furnish us, at 
their earliest convenience, with full abstracts for publication in the Journal. 
In general, the policy pursued for abstracts and reviews will be to employ 
*~™o ~*\*~~ language than that of the original, in order to give those who are 

ead an article in the language in which it is written an opportunity 
acquainted with the main contents. In consequence, abstracts 

ied may at times be translated, not necessarily into English, unless 

expresses his wish to the contrary. 

ire going to press, The University of Chicago announces that the 
his Journal will be in charge of Geophysics at the Yerkes 

Y- 



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RE 11 E IV S 95 

REVIEWS. 

Chree, C: Analysis of the Res ul/! from the Kew Declination and Horizontal 
Force Magnetograph during the selected " Quiet" Days of the Five Years 
1890-Q4. Report of the British Association Committee on Comparison 
and Reduction of Magnetic Observations, Ipswich Meeting, 1895. 

Die in dieser Abhandlung benutzten ruhigen Tage sind die vom Astro- 
nomer Royal ausgewahlten. Dass fur jeden Monat fiinf solche Tage gewahlt 
-sind, giebt allerdings eine erwtinschte Gleichheit der Anzahl, lasst aber 
bcfiirchten, dass der Charakter der Tage weniger einheitlich ist. 

Die Mittel der 25 Stundenwerthe (Mitternacht bis Mitternacht), abgeleitet 
mit Hulfe der jahrlich publizirten Monatsmittel der Stundenwerthe, lieferten 
nicht die erwartete rein cyclische tagliche Variation, sondern ein entschiedenes 
Anwachsen wahrend eines Tages. Der Betrag war, pro Jahr gerechnet, 
4-35' in der Declin. und + 1265x10-5 C.G.S. in Hor. Int. Beilaufig wird 
mitgetheilt, dass umgekehrt die Vert. Int. abnimmt. Mr. Chree halt es fur 
wahrscheinlich, dass diesem nicht-cyclischen Theile eine tagliche Ungleich- 
heit anhaftet, und dass der vorhergehende und der folgende Tag dariiber 
vielleicht mehr Licht geben konnten, hat ihn aber vorlaufig ohne tagliche 
Ungleichheit angenommen. Mittelst des oben citirten Betrages des regel- 
tndssigen Anwachsens wurde nun die gewohnliche tagliche Variation fiir die 
Monate, Quartale, Semester und das Jahr abgeleitet. 

Auf die tagliche Variation fiir Sommer, Winter und Jahr sind harmonische 
Reihen angewendet ; auch sind die Decl. und Hor. Int. in Polarcoordinaten 
umgewandelt und die geschlossenen Tagescurven beigegeben. Um die ver- 
schiedene Grosse der Variation fiir die 12 Monate zu zeigen, giebt Mr. Chree 
die Summe der Stundenabweichungen (ohne Riicksicht auf das Zeichen) und 
die Extreme, und letztere mit und ohne Elimination. 

Schliesslich wird die jahrliche Variation abgeleitet unter Annahme einer 
■constanten Sacular-Variation, und werden die verschiedenen Fehlerursachen, 
welche von ausserlichen Umstanden herrlihren konnen, erwogen. Die werth- 
volle Abhandlung giebt sehr practische Data fiir die Kenntniss des Erdmag- 
netismus und eine nicht bekannte Eigenschaft der ruhigen Tage: die 
nicht-cyclische Variation. Es ist klar, dass dieses Phanomen ganz dasselbe 
ist, als die von mir gefundene Nachslorung, 1 welche auch bei den Normal- 
tagen (fiir Petersburg und andere Stationen) nachgewiesen wurde. Die 
tagliche Ungleichheit dieser NachstSrung zeigte sich sehr bedeutend und 
besonders wahrend der Nachtstunden unregelmassig, so dass der von Mr. 
-Chree benutzte Unterschied der zwei aufeinander folgenden Mitternachts- 
werthe sehr unsicher das Mass des Anwachsens giebt und ein Fortlassen der 
taglichen Ungleichheit einen typischen Einfluss hat. Weiter folgt aus 
meinen Resultaten, dass dieses Anwachsen auch eine jahrliche Schwankung 
zeigt, also nicht fiir alle Monate der gleiche Betrag genommen werden darf. 

Ich benutze die Gelegenheit, mit wenigen Zeilen einige Einwendungen des 
Herrn Professor Bigelow (cf pg. 53, No. 1) zu beantworten. Ich habe bei 
der Ableitung der Nachstbrungsvectoren immer nur die Tages- und Stunden- 
mittel aufeinander folgender Tage verglichen, gerade um die Ungewissheit 
iiber die zu verwendenden Monatsmittel zu umgehen, und habe nur die 
Abweichungen vom Monatsmittel der Uebersichtlichkeit wegen beigegeben. 
Eine lineare Interpolation von Monatsmittel zu Monatsmittel ist hypothetisch, 
andert auch nur wenig an den Resultaten. Fiir die tagliche Ungleichheit 

1 Mcteorohgischc Zeitschrift, September 1895. Ein Vortrag iiber diese Nach- 
storung wurde von mir auf der fiinften Versammlung des Niederlandischen Naturwiss. 
und Mediz. Congresses zu Amsterdam am 19. April 1895 gehalten. 



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96 RE VIE li 'S [Vol. 1 . No. 2] 

verglich ich immer nur zwei (oder drei) aufeinander folgende Tage und hatte 
also keine nennenswerthe saculare Aendyung des Monatsmittels oder der 
normalen taglichen Variation zu furchten. Der exacte Zusammenhang von 
NachstSrung und magnetischem Sturme ist noch nicht klar ; ich freue rnich 
aber, dass Professor Bigelow der Ansicht ist, dass wenigstens die Permanenz 
des Nachstorungspoles auf der Erde mit seiner Theorie nicht unvereinbar ist. 
Auch der Zusammenhang mit dem Nordlichte ist noch nicht gentigend fest- 
gestellt, dass man die Meridiane der Nachstorung "auroral meridians" 
nennen k6nnte. 

Ich hoffe einmal die Gelegenheit zu haben, meine Resultate in umstand- 
licherer Form mitzutheilen, urn sie bessei mit denen der Herren Chree und 
Bigelow vergleichen zu konnen. 

W. van Bemmelen. 



THE POTSDAM ROYAL MAGNETIC OBSERVATORY. 

Veroffentlichungen des Koniglich Preussischen Meteorologtschen Ins ti tuts, 
Heraugegeben durch dessen Director, IV. v. Be sold. Ergebnisse der 
magnetise hen Beobachtungen in Potsdam in den Jahren 18 go und 
1891 von Dr. M. Eschenhagen. Berlin : A. Ascher, 1894, 4 . LXIV+ 
84 pp., 1 1 pi., 5 fi g s - 
This volume constitutes the first publication of observations and results of 
one of the most carefully designed and best equipped of modern magnetic 
observatories. One cannot but be impressed with the extreme care taken by 
all concerned in the location, construction and equipment of the Observatory. 
Great satisfaction must be expressed that it was deemed worth while not 
alone to build well, but also to describe well and minutely every detail con- 
nected with the erection of the Observatory, and the adoption and installation 
of the instruments. As this Observatory, furthermore, represents in a certain 
sense the embodiment of the best thought, as rtsulting from a careful study 
of all similar institutions, future constructors of such observatories will be well 
repaid by a careful perusal of this valuable and suggestive volume. 

The Observatory is located at Potsdam, on the large government reserva- 
tion on the Telegraphenberg, and forms one of the famous group of buildings 
erected by the German Government for the prosecution of astrophysical 
and geophysical investigations, such as the Astrophysical Observatory, the 
Geodetic Institute and the Meteorological-Magnetic Institute. The latter is 
under the general control of Professor von Bezold, Director of the Royal 
Prussian Meteorological Institute at Berlin ; the local direction has been 
assigned to Professor Sprung, while to Professor Eschenhagen has been given 
the especial charge of the Magnetic Observatory. The Observatory is about 
153 meters west of the middle dome of the Astrophysical Observatory, and 
about 120 meters south of the Meteorological Institute, and far removed from 
all industrial disturbing influences. The soil consists of a loose, white sand. 
A preliminary examination could detect no local disturbances. Especial care 
was taken in the erection of the nearest building — the Meteorological Insti- 
tute, which at the same time contains the dwellings of Professors Sprung and 
Eschenhagen — to avoid massive iron masses, such as large iron girders, or 
pipes, iron -staircases, etc., in the construction. Since the building of the 
Magnetic Observatory, several small iron buildings belonging to the other insti- 
tutes have been built at distances of 100 to 200 meters. Although it is 
believed that if any effect whatever is to be felt from these adjuncts, it will be 
extremely small, nevertheless, a careful and quantitative examination is to be 
undertaken. 



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REVIEWS 97 

The general plan of the Observatory, as designed by Professor von Bezold, 
follows closely Mascart's idea of concentrating all the various phases of 
magnetic work in one building instead of in detached buildings, as, e. g. t the 
model Russian Observatory at Pawlowsk. It was found desirable to enlarge 
upon the dimensions employed at Pare St. Maur, and it is suggested that a 
still further enlargement would have been found advantageous. The building 
consists of a basement for the variation instruments and a one-storied super- 
structure for the absolute instruments, the larger dimension of the building 
being in an east to west direction. The question of building material being 
of prime importance this was given especial attention by Professor Sprung, 



who, after many careful tests, selected for the substructure a limestone from 
Rudersdorf, and for the superstructure a fine-grained sandstone from 
Wefensleben. No cement of any kind was used, and of the metals only 
copper and bronze were utilized in the construction of the building. Every 
precaution was taken to guard against moisture and to assure as equable 
and constant a temperature in the observing-rooms as possible. The cellar 
walls are double, with an air-space between them, the inner wall being one 
meter thick, the outer, the face of which is in contact with the earth, being 
specially lined with a protective covering against moisture, three-fourths of a 
meter in thickness. All windows are double and as air-tight as possible ; 
below the roof is an air-space after the Tyrolese fashion for the regulation of 
the radiation of the Sun's heat, the stoves are carefully screened and a special 
system of ventilation is employed for the cellar rooms. The annual tempera- 
ture variation in the magnetograph rooms was thus reduced to 1 1 ° C, the 
daily to o\$ C, while the humidity varied, in the course of the year, between 
60 and 80 per cent. The magnets themselves, since they are placed under 
special covers, are subjected to even a smaller temperature variation. It is 
hoped, however, to make still further improvements. For special observa- 



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9^ RE VIEWS | vol. I , No. *J 

tions, e. g., with large magnets or powerful electric currents, there is in 
addition to the principal building, in which, of course, such observations could 
not be made by reason of the disturbing influence on the recording instruments,, 
a smaller wooden structure about seventy-five meters south of the main build- 
ing. It was possible to begin the regular observations on January I, 1890. 

The general scheme of work as carried out by Professor Eschenhagen and 
one assistant embraces the care of a double system of variation instruments, 
the main, a continuous self-recording one, by means of photographic registra- 
tion, the secondary or check system, adapted to direct eye-reading by means 
of telescope and scale ; the making of the absolute observations three times a 
month ; numerous special investigations ; instrumental adjustments and 
determinations of constants, and finally, the reduction and discussion of the 
observations. It is planned when the working force has been increased, to 
add earth current observations, and to make the Observatory the base station 
of a detailed magnetic resurvey of Germany. The atmospheric electricity 
observations are carried out by the Meteorological Institute proper. 

As special stress was to be laid upon the sensitiveness of the recording 
instruments, preference was given to the Mascart system, in which the 
needles employed are small and sensitive, only 5 cm long and weighing about 
10 grams. It was found desirable, however, for the special purpose at hand,, 
not to adopt the Mascart system of photographic registration whereby three 
elements are recorded on a single paper, one above the other, a single base 
line being common to all, but to have instead, each element recorded separ- 
ately on three different cylinders, each 2o cm wide ; a fourth cylinder being 
likewise added for special investigations. The time scale was lengthened so- 
that 2o mm , instead of i5 ,nm as usual, represented one hour. Professor 
Eschenhagen has succeeded in so perfecting this registration apparatus 
that the photographic traces obtained with it are exceptionally sharp 
and clear, having a width of only o mm .2 to o mm .5. It is thus possible 
to recognize even very minute oscillations such as occur, for example,, 
during thunderstorms or earthquakes, the record of which is frequently 
obliterated in the curves of the Kew system. By the invention of a triple 
mirror arrangement in which the faces of the three mirrors have a slight incli- 
nation to each other, complete records of exceptionally large disturbances can 
be obtained which, on account of the limited width of the cylinder, are fre- 
quently partially lost. For example, in declination a disturbance of 0/ can 
be fully recorded, whereas with the single mirror, disturbances larger than 3 
leave the sheet. This main system of variation instruments is installed in the 
west room of the cellar, while in the east room is to be found the secondary or 
eye-reading system, according to the Wild pattern and constructed by Edel- 
mann, the magnets being about twice the length of those of the main system. 
Readings of all three elements, declination, horizontal and vertical intensity* 
are taken daily, viz., at 10 a.m., i p.m., and 6 P. m. This secondary system 
serves as a check upon the other and also as an intermediate one between 
the absolute instruments and the primary self- registering system. The abso- 
lute determinations are referred first to the secondary variation system by 
means of strictly simultaneous observations made three times a month at an 
average interval of ten days, the exact coincidence in time being secured by 
the pressing of an electric button by the observer at the absolute instru- 
ments, thus causing a small glow lamp (of 10 volts) placed before the observer 
at the secondary variation instruments, to brighten ; this electric signal arrange- 
ment, as it is used, has no appreciable influence upon the variation instru- 
ments. The continuous, relative observations of the primary system are then 
converted into absolute measure by reference to the secondary system with 
the aid of the tri-daily readings. 



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REVIEWS 99 

The absolute observations, as already stated, are made in the west room 
of the first floor. It was found that with the size of the magnets employed the 
disturbing influence upon the variation instruments in the cellar below was of 
such an order that it could be neglected. The general scheme of observation 
is ultimately to consist of a double determination of all three elements, decli- 
nation, horizontal intensity, and inclination, by two independent methods, e.g., 
inclination by means of dip needle and earth inductor, the intensity with the 
magnetic theodolite and by means of the Kohlrausch bifilar-galvanic or mag- 
netic method, and so likewise the declination by means of two methods. It is 
thus hoped to eliminate and determine as far as possible the cause of the 
instrumental differences as revealed by the comparisons of Rijckevorsel, 
Solander and Riicker. Want of space will prevent us from going further 
into detail. Reference will have to be made to the original.* 

The appended tables of hourly values of D, H and V are given in abso- 
lute measure and in C. G. S. units. A fivefold classification of semi-daily 
curves is undertaken, and the hourly value occurring at a time when the 
character of the curve can be conventionally designated as belonging to class 
three, or higher, is indicated in the tables by a special mark, thus rendering it 
easy to pick out disturbances and to form some judgment as to their duration 
and character. 

Special note is made of two classes of disturbances which the fineness and 
distinctness of the Potsdam magnetic traces clearly indicate, viz., those due to 
thunderstorms which in general are not felt by magnetic observatories and 
hence are probably to be referred to local conditions, and secondly two earth- 
quake disturbances, the one felt in Italy, June 7, 1891, and the other in 
Japan, October, 27, 1891. 

From the tabular and the graphical representation of the diurnal distribution 
of disturbed hours, it is found that for all three elements, the principal max- 
imum is reached towards evening between 7 and 9 o'clock, a secondary max- 
imum occurring early in the morning between 2 and 4, while the minimum 
takes place about noon or somewhat earlier. The total sum of disturbed 
hours in 1891 was decidedly larger than in 1890, being thus in conformity 
with the relative numbers of Sun-spot frequency. 

L. A. Bauer. 

Dr. van Rijckevorsel : A Magnetic Survey of the Netherlands for the 

Epoch January /, i8qi. Nieuwe Verhandelingen van het Bataafsch 

Genootschap der proefondervindelijke Wijsbegeerte te Rotterdam. 

Buitengewone Aflevering. Rotterdam 1895. 

Der durch seine magnetischen Vermessungen in Sumatra und Brasilien 

riihmlichst bekannte Verfasser unternahm in den Jahreh i890-'92 auf Anre- 

gung des verstorbenen Buys Ballot eine detaillirte magnetische Aufnahme 

der Niederlande. Bereits i889verglich er seine Instrumente, ein Elliot'sches 

Magnetometer und ein Inclinatorium von Dover, mit den Apparaten der 

Observatorien zu Kew, Pare St. Maur, Utrecht und Wilhelmshaven, wovon 

die Resultate ve'roffentlicht sind in der Schrift "An attempt to compare the 

instruments for absolute magnetic measurements at different observatories," 

herausgegeben in i890vom Meteorologischen Institut zu Utrecht. Es zeigten 

sich ziemlich betrachtliche Differenzen zwischen den Observatorien, welche 

^ee also M. Eschenhagen, "Einige Bemerkungen zur Aufzeichnung der Variati- 
onen des Erdmagnetismus," Meteorologische Zeitschrift, 1892, Vol. VIII., No. 12. Like- 
wise the valuable paper by Professor Eschenhagen "On some improvements in mag- 
netic instruments," published in Part II., p. 539 of the Report of the International 
Meteorological Congress, held at Chicago in 1893, cd. by O. L. Fassig. 



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I OO RE VIE IVS [vol. I . No. 2j 

den Betrag der Beobachtungsfehler liberschritten, und die daher notwendig 
beriicksichtigt werden mussen, wenn man die Aufnahmen verschiedener Lan- 
der zu einer Karte zusammenschmelzen will. 

Durch griindliche Untersuchung seiner eigenen Instrumente, die er 
schon bei seinen friiheren Beobachtungen benutzt hatte, kam R. zu der 
Ansicht, dass dieselben noch mancherlei Verbesserungen fahig sind, da die 
Genauigkeit noch zu wunschen ubrig liess, ebenso muss aber die Controle 
der Variationsinstrumente an den Observatorien noch auf einen grosseren 
Grad der Precision gebracht werden. Eine Untersuchung der sacularen 
Variation in den Niederlanden und den anstossenden Gebieten lieferte ihm 
den Betrag der hierfur anzubringenden Correction, die dieselbe blieb fiir das 
durchforschte Gebiet. Zur Elimination der taglichen Verschiedenheiten der 
magnetischen Elemente dienten die registrirten Curven des magnetischen 
Observatoriums zu Utrecht ; zum Yergleich wurden notigen Falls die der 
anderen oben genannten Observatorien herangezogen. 

Bei den Dcclinationsbestimmungen zeigte sich, dass die Fadenaufhangung 
des Magnets wegen der Torsion im Felde zu Ungenauigkeiten fiihrt; auch ist 
der Wind ein Hinderniss, zumal man auf einer langeren Reise haufig mit der 
Ungunst der Witterung zu kampfen hat. Man sollte — nach Ansicht des 
Referenten- im Felde nur eine Spitzenbewegung der Magnetnadel ver- 
wenden, d. h. die Declinationsnadel, die man auch als abgelenkte Nadel bei 
den Intensitatsbestimmungen benutzt, soil wie eine Compassnadel mit einem 
Hutchen auf einer hinreichend spitz zu erhaltenden Pinne ruhen. Man 
gewinnt dadurch sehr viel ruhigere Bilder beim Einstellen mit dem Fernrohr 
und kann durch leichtes Kratzen mit dem Fingernagel an der Feinschraube 
die Reibuntf der Nadel fast unschadlich machen, so dass im Felde selbst bei 
Wind Einstellungen erzielt, die bis auf 0.5 sicher sind. Der astronomische 
Meridian wurde durch Sonnenbeobachtungen ermittelt, wobei das Sonnen- 
bild durch einen kleinen Spiegel in das Fernrohr geworfen wird. Die Xicht- 
parallelitat von Fernrohraxe und Spiegelaxe wird durch das Beobachtungs- 
verfahren aber nicht vollkommen eliminirt. Zeitbestimmungen wurden nicht 
gemacht, sondern die Zeit einem Chronometer entnommen, das in Utrecht 
mehrfach verglichen wurde. Die fiir Azimuthbestimmungen ungiinstigen 
Mittatjsstunden wurden vermieden. Durch Discussion aller Fehlerquellen, 
niimlich ungenaue Kenntniss der Zeit, Sonnenbeobachtung, Bestimmung des 
magnetischen Meridians und Elimination der Yariationen, kommt der Ver- 
fasser zu dem Resultat, dass der wahrscheinliche Fehler einer Declinations- 
bestimmung etwa 100' betragt. Dieser Werth ist nicht sehr gunstig, verdankt 
aber zur Halfte seine Entstehung der ungenauen Elimination der Yariationen. 

Die Horizontalintensitdt wurde meist sowohl durch Ablenkungen als 
Schwingungen bestimmt. Die Resultate waren recht befriedigend und 
ergeben die Horizontalkraft bis auf circa 0.00005 C.G.S. 

Die Inclination wurde nur relativ, d. h. ohne Ummagnetisiren der vier 
Nadeln, bestimmt und die nothigen Correctionen durch Yergleiche in Utrecht 
bestimmt. Die Endresultate besitzen einen wahrscheinlichen Fehler von 
circa 0.5 '. 

Die Ergebnisse fiir alle drei Elemente, die an den 328 Stationen beob- 
achtet wurden, sind nebst einer Anzahl Einzeldaten in Tabellen wiederge- 
geben, /'. e, so dass man einen guten Ueberblick iiber die mit Sorgfalt durch- 
gefiihrte, umfangreiche Beobachtungsreihe erhiilt. Alle Werthe sind auf die 
Epoche j8qi o reducirt. Da auf circa 100 Quadratkilometer eine Station 
entfallt, so diirfte hiermit das dichteste Netz von dem zur Zeit veroflentlich- 
ten magnetischen Landesvermessungen gewonnen sein. 

Die Resultate sind nun in der Weise in Karten niedergelegt, dass zunachst 
die sogenannten wahren isomagtwtischen Linien gezeichnet wurden, d. h. es 



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REVIEWS 101 

wurden die Linien gleicher Declination, Horizontalintensitat und Inclination 
gezogen, wie sich dieselben moglichst genau den Beobachtungen anpassen, 
ohne also irgend welche Ausgleichungen vorzunehmen. Dasselbe geschah 
auch mit den rechtwinkligen Componenten, Vertikalkraft, Nordliche und 
Westliche Componente, die aus den erstgenannten Bestimmungsstucken sich 
unmittelbar ergeben. 

Da die so gezogenen Linien recht erhebliche Unregelmassigkeiten auf- 
weisen, so war die wichtigste Frage, fur diese letzteren eine Darstellung zu 
gewinnen, aus der der Sitz und die Starke der storenden Krafte ermittelt 
werden konnte. Verfasser hat dazu das bereits erfolgreich von Riicker und 
Thorpe bei der englischen Landesvermessung angewendete Verfahren einge- 
schlagen, mit der Modification, dass er gleich von den rechtwinkligen Com- 
ponenten ausgeht und die von den obengenannten Autoren eingefiihrten 
Districtscurven ableitet. Darunter ist eine rechnerische Ausgleichung der 
beobachteten Werthe eines grosseren Gebietes (Districtes), wozu in diesem 
Falle das ganze Land zusammengefasst wurde, zu verstehen, indem jede 
Station Gleichungen liefert, in denen ein magnetisches Element und beide 
geographische Coordinaten eingefuhrt sind. Man erhalt alsdann glatte, aus- 
geglichene Curven fiir die betreffenden magnetischen Elemente, die im 
Gegensatz zu den wahren isomagnetischen Linien terrestrische (auch berech- 
nete) Linien genannt werden. Auch diese sind vom Verfasser in Karten 
wiedergegeben. Die Abweichungen der beobachteten Componenten von den 
berechneten geben alsdann ein bestimmtes Maas fiir die storende Kraft an 
jeder Station, die wiederum in Karten eingetragen sind und zwar so, dass 
durch eingezeichnete Pfeile die Richtuug und Starke der Horizontalcompo- 
nente der storenden Kraft dargestellt sind, wahrend die Starke der verticalen 
Componente ausser durch Zahlen noch durch mehr oder weniger rothe (fiir 
positive Anomalien) und blaue (fiir negative) Farbung gekennzeichnet sind. 
Auch die Anomalien der Total intensitat sind in gleicher Weise abgeleitet und 
dargestellt. 

Die erwahnten Pfeile deuten immer nach einem Attractionscentrum, das 
auch eine Linie sein kann, wofiir von Riicker der Name ridge line, Kantm- 
linu oder Riickenlinie eingefuhrt ist. Eine solche Linie verliiuft dann gewohn- 
lich auf einem Gebiete positiver Anomalien der Verticalintensitat, im Gegen- 
satz zu den Thallinien, valley lines \ von denen jene Pfeile scheinbar ausgehen, 
und die Minderwerthe der Verticalkraft besitzen. Die kartographische Dar- 
stellung dieser Linien, an denen das durchgeforschte Gebiet sehr reich ist, 
bietet dem Verf. zu interessanten Betrachtungen Anlass. Bei der Einfach- 
heit der geologischen Verhaltnisse des Landes, die keine magnetischen 
Gesteinsforma ionen von Belang aufweisen, ist man genothigt, in der Tiefe 
solche Massen anzunehmen, die, wie Verf. andeutet, vielleicht gerade der 
hollandischen Kiiste eine gewisse Festigkeit gegen den Wogenprall geben. 
Besonders auffallend ist eine Kammlinie, die von der Insel Wieningen, dies- 
seits der Inseln Texel, Vlieland, Terschelling und Ameland, verlauft. Im 
Siiden setzt sie sich diesseits fort zu einem Gebiet starkster verticaler Stoning 
siidostlich von Utrecht. Ein Gebiet sehr schwacher Verticalkraft befindet 
sich in der Nahe von Groningen. Wir konnen hier ohne kartographische 
Darstellung keine vollkommene Darstellung der interessanten Verhaltnisse 
geben, mochten aber dem Verfasser vollstandig beipflichten in der Meinung, 
dass eine Beantwortung der Fragen nach dem Ursprung solcher Storungsge- 
biete, die unzweifelhaft einen wichtigen Fingerzeig fiii die Verhaltnisse des 
Erdinnern geben, nur dann geschehen kann, wenn auch eine Durchforschung 
der Meerestheile mit entsprechender Genauigkeit stattgefunden hat. 

Schliesslich mochte Referent noch die Ansicht hinzufugen, dass die 
Ursachen solcher grosserer Storungen, die Riicker "regional-" und "district 



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102 REVIEWS 



[Vol. I. No. 2 J 



disturbances" nennt, vielleicht nicht ausschliesslich im Gesteins- odtr Gebirgs- 
magnetismus ihren Grund haben, sondern dass die Vertheilung von Land un 
IVasser, oder allgemein auch die verschiedene Leitungsfahigkeit des Erd- 
bodens, die Erdstrome und damit den Erdmagnetismus beinflusst. Bet dem 
auffallend differenten Verhalten, welches diese Vertheilung im grossen in 
Folge der Configuration der Continente zeigt, ist es moglich, dass Einflusse 
•sogar schon an verhaltnissmassig kleinen Kiisten und Inseln bestehen, ja 
vielleicht ist bei continentalen Verhaltnissen der Einfluss von Wasserzugen in 
gewissen Tiefen der Erdkruste von Einfluss. Im Falle der Richtigkeit dieser 
Behauptung wurde man auf hoher See den gleichmassigsten Verlauf der 
Erdstrome und damit auch die gleichmassigste V r ertheilung des Erdmagne- 
tismus beobachten mlissen. 

M. ESCHENHAGEN. 



TERRESTRIAL MAGNETISM AT THE INTERNATIONAL METE- 
OROLOGICAL CONGRESS HELD AT CHICAGO, 1893. 

The papers presented at this meeting, held under the auspices of the 
Congress Auxiliary of the World's Columbian Exposition, are being pub- 
lished as Bulletin No. 1 1 of the United States Weather Bureau, under the 
editorship of the secretary of the congress, Mr. O. L. Fassig. The Parts I. 
and II., containing the papers with which this Journal is concerned, have 
now appeared. It is intended to bring later brief abstracts of the various 
articles ; at present only the titles can be given. 

In Part I., Af. A. Veeder: An international cipher code for correspond- 
ence respecting the aurora and related conditions, p. 26 ; G. IV. Littlehales, 
The secular change in the direction of the magnetic needle ; its cause and 

period, p. 1 74- 

In Part II., G. Hcllmann: Contribution to the bibliography of meteorol- 
ogy and terrestrial magnetism in the fifteenth, sixteenth and sevententh cen- 
turies, p. 352 ; C. A. Schott, Magnetic survey of North America, p. 460; A. 
de Tillo* Magnetic survey of Europe and Asia, p. 465 ; C. Borgen.The inter- 
national' polar expeditions, 1882-3, p. 469 ; T. Bertelh, The discovery of the 
magnetic declination made by Christopher Columbus, p. 486; S. Lemstrom, 
The roHinical relations manifested in the simultaneous disturbances of the 
nun, the aurora and the terrestrial magnetic field, p. 492 ; F. H. Bigel<m* t 
| hr periodic terms in meteorology due to the rotation of the sun on its axis, p. 
*oo ; J. EMrrvauX H. GeiUl, Review of recent investigations into the subject 
ti\ iihiioHpheric electricity, p. 510; Af. Th. Edelmann, On the construction of 
«*;«rtli magnetic instruments, p. 522; Af. Eschcnhagen, On some -improve - 
ifiriiiH in magnetic instruments, p. 539; A. Schuster, The present condition of 
mathematical analysis as applied to terrestrial magnetism, p. 550; A. B. 
( 'haitveau. Methods and instruments of precision for the study of atmospheric 
rl«< tri< ity, p. 569. An elaborate paper prepared by Professor G. Neumayer % 
"On the Cartographic Presentation of the Distribution of the Forces of Ter- 
r^ntrial Magnetism and their Variations, including a brief abstract, at his 

ation, of the results of the investigations on the secular motion of a free 

die needle by L. A. Bauer, was lost in transmission. 



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PUBLfCAT/OXS 10? 



PUBLICATIONS.' 



van Bemmelen, W. Allgemeine Graphische Darstellung der Sakular- Variation der 

Erdmagnetischen Deklination. Publ. by Author, Utrecht, 1895. 24x29.5 cra . 

Pp. 4. One insert. 
. Die Linien gleicher Sakular-Variation der Declination. Repr. Versl. K. 

Akad. van Wetenschappen te Amsterdam, van 30 Nov. 1895. x 7«5 x 26 cm . Pp. 6. 

One insert. 
von Bezold, W. Der normale Erdmagnetismus. Sitzber. Akad. Wiss. Berlin, 

Dec. '95. Pp. 1119-1134. 
Carlheim-Gyllenskold, V. Determinations des e*16ments magne*tiques effectue*es 

sur la glace de quelques lacs en Suede pendant l'hiver 1889. Bihang till K. 

Svenska Vet.- Akad. Handlingar. Bd. 20, Afd. 1, No. 8. Stockholm, 1895. 

I4x2i«n. Pp. 32. 
. Observations magne*tiques faites par Th. Arwidsson sur les c6tes de la Suede 

pendant les annles 1 860-1. K. Svenska Vetensk.-Akad. Handlingar. Bd. 27, 

No. 8. Stockholm, 1895. 24x29.5"°. Pp.22. 
Folgheraiter, G. Intensita Orrizontale del Magnetismo Terrestre lungo il Parallelo 

di Roma. Nota. Frammenti concernenti la Geofisica dei Pressi di Roma, 

N. 2. Roma, 1896. 18.5x26.5"". Pp.9. 
Fritsche, H. Uber den Zusammenhang zwischen der erdmagnetischen Horizontal- 

intensitat und der Inclination. Mit einem Anhange von 29 Tafeln. St Peters- 
burg, 1895. I4.5x23 cra . Pp. 14+28. 
Keller, F. SulP Intensita Orizzontale del Magnetismo Terrestre nei Pressi di Roma. 

Frammenti concernenti la Geofisica dei Pressi di Roma. N. 1. Roma, 1895. 

I9x27 cro . Pp. 11. 
Klossowsky, A. Annales de l'Observatoire Me*te*orologique et Magn&ique de 

l'Universite* Impe*riale a Odessa, pour 1894. Odessa, 1895. 26x3i.5 cm . 
Palazzo, L. Misure assolute degli elementi del magnetismo terrestre eseguite in 

Italia negli anni 1888 e 1889. Repr. Annali dell' Uff. Centr. Met. e Geod., Vol. 

16, Pt. 1, 1894- Roma, 1895. 24x33™. Pp. 151. 
Raja, Michele. Sull' Excursione Diurna della Declinazione Magnetica a Milano in 

Relazione col Periodo delle Macchie Solari. Nota. Estratto dai " Rendiconti " 

del R. Istituto Lombardo, serie 2, vol. 28, 1895. 15.5x23°™. Pp. 15. 
Schmidt, A,dolf. Mitteilungen iiber eine neue Berechnung des erdmagnetischen 

Potentials. Repr. Abhandl. d. bayer. Akad. d. Wiss. II. CI., XIX. Bd., 1 Abth. 

Miinchen, 1895. 22 x 27.5"". Pp. 66. 
Schmidt, Friederich. Der tagliche Gang der erdmagnetischen Kraft in Wien fiir 

die einzelnen Monate der Jahre 1 879-1888, dargestellt durch .periodische Reihen. 

23x29 cm . Repr. Pp. 90-103. 
Schuster, Arthur. Atmospheric Electricity. Lecture before Royal Inst, of Great 

Britain, Feb. 22, 1895. Repr. I3.5x2i cm . Pp. 17. 
de Tillo, Alexis. Atlas des isanomales et des variations slculaires du magne*tisme 

terrestre. Hommage a l'Institut de France. St. Pdtersbourg, 1895. 27 x 35 cm . 

Pp. 4 ; 16 charts. [For the epoch 1859.] 
. Tables fondamentales du magnltisme terrestre. Repartition. Isano- 
males. Ephe*me* rides. Variation Sdculaire. Magnltisme Moyen. St. Pe*ters- 

bourg, 1896. 25 x 33-5 cm . Pp. 6 + 93. 

Cartes des isonamales du magne*tisme terrestre pour l'dpoque 1885. Publ. 



by the Socie"te* Me*te*orologique de France, 1895. 4 charts. 

'Not as yet otherwise noticed in the Journal. As the conventional sizes of 
publications vary so considerably, it has been decided to give the actual outside dimen- 
sions, viz., the breadth and length, the former being given first. 



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LIST OF ASSOCIATES 



Abbe, Cleveland, *rof., United States Weather Bureau, Washington, D. C. 
Baracchi, Pietro, Acting Gov't Ast'r to the Colony of Victoria, Melbourne. 
Bezold, Wilhelm von, Geheimrat, Dir., K. Preuss. Meteorol. Institut, Berlin. 
Biese, Ernst, Director, Meteorological Observatory, Helsingfors, Finland. 
Bigelow, Frank H., Prof., United States Weather Bureau, Washington, D. C. 
BOrgen, C, Prof., Vorstand, K. Man ne-Observatori urns, Wilhelmshaven. 
Chistoni, Ciro, Professor di Fisica nella R. Universita di Modena, Italy. 
Doberck, William, Director of Hong-Kong Observatory, China. 
Eschenhagen, Max, Prof., K. Preuss. Meteorol.- Mag. Obs., Potsdam. 
Hann, Julius, Hofrat, Dir., K. K. Central-Anstalt fiir Met. u. Erdmag., Vienna. 
Hellmann, Gustav, Prof., Vice-Director, K. Preuss. Meteorol. Inst., Berlin. 
Hepites, Stefan C, Director, Roumanian Meteorol. Institut, Bucharest. 
Goldhammer, Dimitry A., Professor, University of Kasan, Russia. 
Lancaster, A., M£teorologiste-Inspecteur, Royal Obs., Uccle, Belgium. 
Lagrange, C, Magnetic Observer, Royal Observatory, Uccle, Belgium. 
Lemstrom, Selim, Professor of Physics, University of Helsingfors, Finland. 
Littlehales, G. W., Chief, Div. Chart Constr., U. S. Hydrographic Office. 
Liznar, Joseph, Dr., K. K. Central -A nsalt fiir Meteorol. u. Erdmag, Vienna. 
Mascart, E., Membre de Tlnstitut, Dir., Bur. Centr. Meteorol., Paris. 
Mendenhall, Thomas C, President Worcester Polytechnic Institute, Mass. 
Moureaux, Th., Chef du Service magne't. a V Obs. du Pare St.-Maur, pres Paris. 
Neumayer, G., Geheimadmiralitatsrat, Director, Seewarte, Hamburg. 
Nipher, Francis E., Prof, of Physics, Washington University, St. Louis, Mo. 
Palazzo, Luigi, Prof., R. Ufficio Centrale di Meteorologia, Rome, Italy. 
Rijckevorsel, van, Dr., Conducting Magnetic Survey of the Netherlands. 
Rucker, Arthur W., F.R.S., Prof, of Physics, Royal Coll. of Sci., London. 
Schering, Ernst, Geheimrat, Dir. Gauss Magnetic Observatory, Gottingen. 
Schmidt, Adolf, Doctor, Gymnasiallehrer, Gotha, Germany. 
Schott, Charles A., Assist, U. S. Coast and Geod. Survey, Washington, D. C. 
Schuster, Arthur, F.R.S., Professor of Physics, Owens College, Manchester. 
Snellen, Mauritz, Chief Dir., R. Meteorol. Inst, of Netherlands, Utrecht. 
Solander, E., Lektor, Wenersborg, Sweden. 

Stok, I. P. van der, Director of Meteorol.- Mag. Obs., Batavia, Java. 
Stupart, R. F., Dir., Mag. Obs., Toronto and of Meteorol. Service of Canada. 
Tillo x Alexis de, G£ne>al de Division, Excellence, St. Petersburg, Russia. 
Wild, Heinrich, Professor, Zurich, Switzerland. 



104 



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TERRESTRIAL MAGNETISM 

AN INTERNATIONAL QUARTERLY JOURNAL 

ItheneT 



PUBLIC Lj L , k ;. f J 



VOLUME I JULY, IOQO I NUMBe!* 3 

1 ASTOR, LCKT.y ,. | 



TlLCi 



N F- 



A SUMMARY OF THE RESULTS OF THE RECENT 
MAGNETIC SURVEY OF GREAT BRITAIN AND 
IRELAND CONDUCTED BY PROFESSORS ROCKER 
AND THORPE. 

By A. W. Rucker, F.R.S. 
Professor of Physics in the Royal College of Science, South Kensington, London. 

PART I. 

ON THE ACCURACY OF THE DELINEATION OF THE TER- 
RESTRIAL ISOMAGNETIC LINES. 

My friend Dr. Thorpe and I have completed a Magnetic 
Survey of the United Kingdom of Great Britain and Ireland, of 
which a full account has recently been published in the Trans- 
actions of the Royal Society. I do not propose in this article 
to give a detailed description of our work, but there are certain 
points which we have been able to discuss with unusual fulness, 
an account of which may be interesting. 

Observations have been made by us or under our direction at 
882 places in the British Isles. There is therefore one station 
to every 1 39 square miles of land area. 

In the first instance we ourselves observed at 205 places, 
between the years 1884-8. 

This completed our First Survey the epoch of which was Jan. 
1, 1886. The results were published in the Philosophical Trans- 
actions (1890 A. p. 53). The Government Grant Committee of 
the Royal Society then supplied us with a liberal subsidy to meet 
the cost of carrying on the work on a larger scale. We obtained 

105 



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106 A. IV. RUCKER [Vol. I. No. 3] 

the services of two assistants, Messrs. P. H. Gray and A. E. 
Briscoe, of whom the latter, on his retirement in 1890, was 
replaced by Mr. W. Watson. The work of these gentlemen was 
of a very high quality and with their aid, in the four years 1 889- 
92, the grand total of the number of stations was brought up to 
882. The additional 677 stations constitute our Second Survey 
the epoch of which is Jan. 1, 1891. 

We believe that in no previous case have two such detailed 
surveys of the same area been made within so short an interval 
of time. They therefore afford a good opportunity of testing 
the accuracy with which the positions of the terrestrial isomag- 
netics can be inferred from the observations. 

To explain how this test was applied it is necessary to describe 
(1) how the terrestrial isomagnetics were drawn, (2) how they 
were reduced to the same epoch. In discussing these curves I 
shall confine my attention to the Declination as precisely similar 
methods were used for the Horizontal Force and Dip. 

(i) THE TERRESTRIAL ISOMAGNETICS. 

In both Surveys the country was divided into nine overlapping 
districts, bounded by fixed lines of latitude and longitude, which 
were the same in each case. 

The stations in each district were weighted, so as to make 
the weighted number of stations per unit of area about the same 
everywhere. The point corresponding to the mean of the 
weighted latitudes and longitudes of all the stations in a district 
was called the central station, and the mean of the weighted 
Declinations was taken as the Declination at that point. The 
rates of change of the Declination per degree of latitude and 
longitude were then calculated on the supposition that they were 
uniform over the whole of each district. Thus the central sta- 
tion of Scotland in the 1891 Survey was at Lat. 56 38' .2 N. 
and Long. 4 21' .5 W., and the declination at any place in 
this district of which the latitude and longitude are / and \ 
respectively is given by the formula 

8=20° 58'. 4+ 13'. 1 (/- 56.6367) + 32-.5 (A-4.3583) 
where / and A are to be expressed in degrees and fractions of a 
degree. 



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r w. 




6" w. 


2t° 12'. 6 




20° 40' .4 


21 8 .4 




20 37 .5 


2t 6 .7 




20 36 .0 


21 9 .2 




20 38 .0 


e points 


were 


determined 



THE MA GNETIC SURVEY OF GREA T BRITAIN 107 

By means of this and similar formulae the Declination 
was calculated for points within the United Kingdom, which are 
defined by whole degrees of longtitude and half degrees of lati- 
tude. All these values are given in a Table of which the follow- 
ing is a sample taken from a region where three districts overlap. 
The figures in parentheses, at the beginning or end of a row, 
indicate the number of the district from which the figures in the 
row were deduced. Where two or more districts overlap, the 
individual Declinations are given in italics, and the means in 
ordinary type. 

Latitude Longitude 

(6) 
52° 30' 21 8 .4 20 37 -S (8) 

(9) 
(Mean) 

From this Table the points were determined where the 
isogonals corresponding to whole degrees of Declination cut the 
lines of latitude, the calculations being made on the assumption 
that the rate of change of Declination with longitude is constant 
within a range not exceeding one degree of longitude. Thus 
the above figures show that the 21 isogonal cuts latitude 52 30' 
in longitude 

6° + ^=6 J .705 = 6 42'. 3 . 

The lines drawn on a map by joining these points are not 
continuous curves. The irregularities are due to the facts that 
some of the nine districts are affected with magnetic disturbances 
which extend over large fractions of their areas, and that in 
some places, especially near the coast, the calculated Declina- 
tions depend upon one district only. The discontinuous isogonals 
so obtained are called the district lines or sometimes the district 
curves. 

The next step was to obtain a formula which should express 

(1) the values of the Declinations at the Central stations and 

(2) the forms of smooth curves representing the general direc- 
tion of the broken district lines. 

Such a formula has no theoretical value. It is often very 
complicated, and sometimes it is best to employ two formulae 



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108 A. W. RUCKER [Vol. I. No. 3] 

for different parts of the kingdom. In spite of these drawbacks 
it is better to use an algebraical expression than to draw smooth 
curves free hand, partly because irregularities which affect a 
large part of one or more isogonals are thus more easily cor- 
rected, and partly because the necessary extrapolation near the 
coast line is best made in accordance with the fixed rule, which 
the formula supplies. 

Thus the equation to the Terrestrial Isogonals south of Lat. 
54 30' N. on Jan. 1, 1891, is 

8= 18 37' + i8'.5 (/— 49.5)-3'-5 cos [45° (/- 49-S>] 

+ 06'. 3 +i'.5(/-49.5)] (*-4) 

+ o'.oi (A -4)' X (Z-54.5) 8 
North of Lat. 54 30' the same expression holds good if the 
last term, i. e., o'.oi (A — 4)' X (/ — 54-5) a be omitted. The 
symbols /and A indicate the latitude and longitude of the place at 
which the Declination is to be determined both expressed in 
degrees and fractions of a degree. 

By means of this formula the Declinations were calculated 
at all points given by the intersections of lines corresponding to 
entire degrees of latitude and longitude. The numbers thus 
found, together with the differences between them were entered 
in a Table of which the following is a sample : 

Latitude 

55' 23° 47'. 4 3*' >* 2 3° "'.8 34-5 

2j'.6 24' ./ 

54' 23 2I'.8 33' .t 22 48 '.7 33.0 

26.7 25.4 

53" 22 55'. 1 3/'.8 22° 23'.3 3/'.8 

28 ' .0 26' .9 

By means of this Table it was easy to calculate the Declina- 

at any given place, using the method of proportional parts. 

The evidence for the satisfactory character of the formula 

of the Table deduced from it is, firstly, that the Declinations 

the central stations calculated from the Table are in close 

:>rd with those deduced from the observations. The average 

erence in the nine cases (taken irrespective of sign) is i'.2 

the greatest difference is 3'. The corresponding numbers 



io° W. 


Longitude 


9 W. 
*3-4 


23° 47 '.4 


34' >6 


23° 12' 


2J ' .6 




24.1 


23 2I'.8 


33'f 


22° 48' 


26'. 7 




25 -4 


22 55'. 1 


3i'-8 


22° 23' 


28 '.0 




26' .9 



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THE MAGNETIC SURVEY OF GREAT BRITAIN 109 

for the Horizontal Force were 0.00005 and 0.00013 C. G. S. 
units, and for the Dip i'.i and 2 '.2. 

Secondly, the isogonal curves deduced from this Table, in the. 
same way as the district lines were deduced from that previously 
described, are continuous, and follow the general course of the 
districtlines, except in places where the latter are obviously irreg- 
ular. The greatest divergence is in the North of Scotland where 
the local disturbances are undoubtedly very large. The curves 
thus determined are called the terrestrial isogonals for 1886 or 
1 89 1 according as they are deduced from the First or Second 
Survey. 

DETERMINATION OF THE SECULAR CHANGE. 

It was next necessary to combine the two Surveys by reduc- 
ing them to a common epoch, and as the number of stations in 
the 1886 Survey is comparatively small (205) a great saving of 
labor was effected by reducing the 1 886 Survey to the epoch 
1 891.0, instead of choosing an intermediate date, which would 
have involved applying corrections to all the results obtained in 
both Surveys. The systematic differences, if any exist, would 
be the same in either case, and the more laborious method has 
therefore no counterbalancing advantage to recommend it. It 
was thus necessary to determine the secular change between 
1886.0 and 1 891.0 as accurately as possible. 

Three sets of data have been utilized for this purpose. 

(i) SECULAR CHANGE FROM CENTRAL STATIONS. 

The central stations in the nine districts from which the district 
lines were determined in the two Surveys differ but little in posi- 
tion. The small corrections necessary to transfer the values of the 
elements obtained at the central stations of the 1886 Survey to 
the positions of the central stations in 1891 cannot introduce 
important errors. Hence the secular change for the five years 
1886.0 to 1 891.0 can be accurately determined at these nine 
points, and as the values of the Declinations at the Central sta- 
tions are deduced from the means of the results at a large 
number of places, the effects of experimental errors, and of any 
purely local effects, are eliminated. 



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no 



A, W. RUCKER 



[Vol. I, No. 3 1 



(2) SECULAR CHANGE FROM REPEAT STATIONS. 

As all the central stations He at some distance from the coast 
it was desirable that the evidence deduced from them should be 
reinforced by observations taken near the borders of the area we 
were studying. 

In 1892, therefore, observations were made at 26 stations, 
which had been included in the earlier Survey. These were not 
scattered uniformly all over the country, but were divided into 
small groups near the coast. The mean value of the secular 
changes observed at each group of stations was assigned to the 
position defined by means of their latitudes and longitudes. 

The groups were lettered from A to G. The secular change was 
taken not from the observations reduced to January 1, 1886 and 
1 89 1 respectively, but over the whole interval which elapsed 
between the two sets of observations at the same station. 

From this the secular change for five years was calculated on 
the hypothesis that the rate of change had been constant during 
the interval in question. 

The difference between the results obtained at neighboring 
stations are certainly in some cases much larger than can be 
accounted for by the mere accumulation of errors of experiment. 
They suggest that the question of the existence of small periodic 
variations in the rate of secular change requires more attention 
than has hitherto been devoted to it. 

(3) SECULAR CHANGE FROM MAGNETIC OBSERVATORIES. 

The third group of data at our disposal for the determination 
of the secular change was furnished by the magnetic observa- 
tories. There are now five of these in the United Kingdom, viz., 
Greenwich, Kew, Stonyhurst, Valentia, and Falmouth. 

Observations were not made regularly at the last two until 
after 1886, so that they do not provide a measure of the secular 
change from 1886-91. 

As Greenwich and Kew are very near together, and as the 
final results of the Greenwich observations for 189 1 were not 
published at the end of 1892, when the secular change was being 
calculated, we have depended only on Kew for the South of 
England, and Stonyhurst for the North. 



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THE MAGNETIC SURVEY OF GREA T BRITAIN 1 1 1 

The data for Stonyhurst were kindly supplied to us by the 
Rev. W. Sidgreaves. 

Having thus collected all the facts which seemed likely to 
be useful, we prepared a Table of the secular changes at the 
intersections of lines corresponding to whole degrees of latitude 
and longitude, so as to secure a tolerably regular variation of 
the change over the whole country, and also to agree as nearly 
as may be with the results of observation as deduced from the 
central stations, repeat stations, and observatories. We therefore 
arranged these in eight secondary groups according to their 
geographical position. In two cases a secondary group consists 
of only one central station. 

As an example I give the comparison between the observed 
secular change in five years deduced from the two groups of 
repeat stations (A and B) and the central station (I) which form 
the secondary group of stations situated in Scotland. 

SECULAR CHANGE 1 886- 1 89 1. 





Declination 




Dip 




Horizontal Force 




Observed 


Table 


Observed 




Table 


Observed Table 


Group A 


-38 '.0 


-38'7 


-4'-5 




- 4 '.6 


-f-0.00089 +0.00 100 


Group B 


-36 .8 


-39 .8' 


-3 .6 




-5 .2 


83 106 


C. S. I. 


—39 -2 


-37 9 


-5 -6 




—5 .3 


128 103 


Mean 


—38 .0 


-38 .8 


-4 .6 




-5 -o 


100 103 



This and other similar results proved that the Table of Secular 
Change was, in each district, in close accord with the means of 
the different values of the secular change obtained in that district ; 
while the means of all the eight secondary groups were as fol- 
lows : 

Observed Table 

Declination —36 '.4 — 36 '.1 

Dip — 6'.2 — 6'.3 

Horizontal Force +0.00105 +0.00106 

We thus obtained a Table of Secular Change which agrees 
closely with the average result of observation over the whole 
area of the Survey, and assured ourselves that this agreement is 
not due to serious errors in different parts of the country neutral- 
izing each other. That these precautions were necessary is evi- 
dent from the fact that the change of declination in five years 
varied from 29'.! in the extreme southeast of England, to 42 '.3 



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112 A. W. RUCKER [Vol. I, No. 3] 

in the northwest of Scotland. In like manner the change of 
Dip was 4'.o in the northeast of Scotland, and 8'.o in the south- 
west of Ireland, while that of the Horizontal Force was 0.00090 
in East Anglia and 0.00122 in southwest Ireland. 

These details as to the methods of drawing the terrestrial 
isomagnetics and determining the secular change are given, to 
show that these operations were conducted in a methodical way 
and that an attempt was made to follow definite rules of pro- 
cedure. We may now pass on to consider the results of the 
comparison of the two sets of isomagnetics obtained by the two 
Surveys. 

COMPARISON OF THE ISOMAGNETICS. 

In the account of our earlier Survey we published tables of 
the calculated values of the elements at the intersections of the 
whole degrees of latitude and longitude for the epoch 1 886.0. 

By adding (algebraically) to these the secular changes for the 
five years 1886-91 taken from the Table described above we 
obtain values which, if the terrestrial isomagnetics for 1886 and 
1 89 1 were absolutely correct, and if the secular change had been 
perfectly determined, would agree with the numbers in the cor- 
responding Table obtained quite independently from the second 
Survey for the epoch 1 891.0. This precise agreement cannot 
be attained in practice, and the differences between the values 
deduced from the two calculations serve as a measure of the 
accuracy with which the calculated values of the elements can be 
determined when freed from the effects of local disturbance. In 
the full paper we make this comparison at 91 points, of which a 
few are in the sea at some little distance from the coast, so that 
the test is a severe one. It must also be remembered that the 
irregular shape of the British Isles adds very much to the diffi- 
culty of determining accurately the positions of the isomagnetics. 
In the following Table, therefore, I give not only the numbers 
which refer to all the points of comparison but also those deduced 
from 28 points which, though some of them lie in the Irish Sea, 
are remote from the external coast line, and are therefore distant 
from the border of the Survey. These points are regularly dis- 
tributed on or within the following lines, Xat. 52 , Long. 2° 



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THE MA GNETIC SURVEY OF GREA T BRITAIN 1 1 3 

W., Lat. 55 and Long. 8 Q W. In the Table the average differ- 
ences are of course taken without reference to sign. 

Average difference between the two calculated values Corresponding distances 
of the elements at in miles between the two 

(i) All points (2) 38 internal points setsof isomagnetics 

Declination i'.4 i'.i 1.7 1.4 

H (C. G. S.) 0.00022 0.00011 4.0 2.0 

Dip 1 '.3 o'.g 2.6 1.8 

Mean . . . . 2.8 1.7 

It appears from this Table that we have been least successful 
with the lines of equal Horizontal Force, for the equation to 
which we found some difficulty in obtaining a satisfactory 
expression. 

The general conclusion seems to be that if two perfectly inde- 
pendent determinations of the positions of the terrestrial isomag- 
netics are made five years apart, and reduced to the same epoch 
by such means as we adopted, the average distance between either 
of the two sets of lines and the mean of the two will not exceed 
a mile and a half (say 2.2 kilometers) even when the survey is that 
of a country, which, like the United Kingdom, is very irregular in 
outline, and includes relatively large areas of basalt on which 
there are very great local disturbances. 

In the center of the region surveyed, the doubt as to the true 
position of the lines need not, on the average, exceed 1 500 yards 
(say 1.4 kilometers). 

Of course these magnitudes will in part depend on the change 
per degree of the magnetic element in the district under consid- 
eration, but they may serve as illustrating the order of the 
accuracy which is attainable. 

The largest differences between the positions of two corres- 
ponding lines rarely exceeded twice the average difference, and the 
positions at which they occurred were always either without or 
just within the coast line. 

It is interesting to compare the average deviation from the 
mean of the calculated values of the elements at the 28 internal 
points, with the probable error of the observations. In calculat- 
ing this latter quantity we deal only with observations made in 
the field, on the same spot, and in most cases on the same day. 
Some sources of error are therefore excluded which affect the 



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114 



A. W. RUCKER 



[Vol. I, No. 3 J 



results when the operations are repeated after relatively long 
intervals of time, with different instruments and by different 
observers, and therefore perhaps not exactly in the same position. 
The comparison as made with this restriction is exhibited below. 



Declination 
H (C. G. S.) 
Dip 



Probable error of 
observed values 

±l 0.6 

zb 0.00006 
d= 0.4 



Deviation from the mean 
of the calculated values 

± o'.55 
rh 0.000055 

± o'-45 



Hence we arrive at a result, which must be regarded as satis- 
factory, that the accuracy of the calculated values is about equal 
to the probable error of an observation when both are determined 
under the most favorable conditions. A further discussion of 
the magnitude of the errors of experiment which may arise when 
this limitation is withdrawn will be found in the next section. 
As the errors are then much larger, the proof that the method 
of calculating the undisturbed values of the magnetic elements 
is sufficiently good is even stronger than that supplied by the 
above figures. 

PART II. 

ON THE ACCURACY OF THE DETERMINATION OF THE 
LOCAL DISTURBING MAGNETIC FORCES. 

It need hardly be said that the main object of so elaborate 
a Survey as that we have carried out was not so much to define 
the precise positions of the terrestrial isomagnetics, though this 
was essential to our purpose, as to study local magnetic disturb- 
ances. The method we adopted for determining the Disturbing 
Forces at any given place was the simplest and most obvious, 
but, as far as we are aware, it had not previously been used in 
working up surveys of districts as large as the United Kingdom. 
The magnetic elements given by direct observation were the 
Declination, Horizontal Force, and Dip. From these the 
northerly, westerly, and vertical components of the magnetic 
force were determined. The calculated values of the same 
quantities for the same geographical position were found from 
the formulae or tables described above. The differences between 
these quantities gave the corresponding components of the Dis- 



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THE MA GNE TIC SURVEY OF GREA T BRITAIN 1 1 5 

turbing Force, and from the first two of these the magnitude of 
the resultant Horizontal Disturbing Force and the angle it made 
with the geographical meridian were determined. The Vertical 
Disturbing Forces were taken as positive when they urged the 
north-seeking pole of the needle downwards. These values were 
entered on a map, positive disturbances being indicated by red, 
and negative by blue figures. Lines, called respectively ridge 
and valley lines, were then drawn through the loci of maximum 
and minimum Vertical Disturbing Force. The Horizontal Dis- 
turbing Forces were depicted by arrows, and it was found that 
(with few exceptions) these were directed to the ridge lines. The 
directions of the arrows at the stations through which the ridge 
lines passed enabled us to correct the positions of the lines, by 
moving them to that side of any station towards which the arrow 
pointed. 

These operations were first performed in the case of our 
earlier Survey, the data at our disposal being those derived from 
205 stations only. Of course it was to be expected that the 
additional information since acquired would add to our knowl- 
edge of details, but it appeared to us to be of great importance 
to determine whether the second Survey when treated quite 
independently led to the same conclusions as to the positions of 
the districts from which the principal Disturbing Forces ema- 
nated. 

Eight such regions were detected in our earlier Survey. In 
them the two independent tests of the existence of a locus of 
magnetic attraction were satisfied, viz., that the Vertical Disturb- 
ing Force over it is higher than at neighboring places, and that 
the Horizontal Disturbing Forces are directed towards it from 
each side. It is satisfactory to be able to state that these two 
conditions are both fulfilled by the later Survey with regard to 
the same districts, which are again shown to be the most impor- 
tant magnetic features of the United Kingdom. The only region 
in which our previous conclusions appear not to be in exact 
accord with the facts is near the Hebrides. There is there some 
doubt as to the direction of a ridge line of which a considerable 
portion must, in any case, run beneath the sea. The agreement 
between the two Surveys, when treated as independent, and each 



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116 A. W. RUCKER [Vol. I, No. 3] 

reduced to its own epoch, is illustrated in our paper by a map 
on which the positions of the eight ridge lines are shown as 
deduced from the earlier and later investigations respectively. 

If, however, as is most desirable, the whole of our work is to 
be reduced to one epoch it is important to. remember that the 
differences between the isomagnetics deduced from the two 
surveys will affect the absolute values of the disturbing forces, 
even if they do not interfere seriously with their relative values 
at neighboring stations. 

Thus confining our attention at first to the vertical disturb- 
ance it is very convenient to regard this quantity as fixing the 
magnetic level or elevation of a place. This elevation is measured 
from an arbitrary datum plane, the position of which is deter- 
mined by the terrestrial lines of Equal Horizontal Force and 
Dip. The two surveys might and do agree in indicating the 
same districts as those of high magnetic elevation, but unless the 
heights are measured from the same datum we cannot, without risk 
of serious error, combine them in tracing ridge or valley lines. 
It is also improbable that the difference between the two planes 
of reference would in general be the same everywhere. We 
should rather expect that they would be inclined to each other 
at a small angle. These considerations are the more important 
since the absolute differences between the two calculated values 
of the Horizontal Force are, in the case of the Vertical Force, 
multiplied by the tangent of the angle of Dip which, in Great 
Britain, varies between 2.5 and 3. Hence we find that between 
the North Sea and the Atlantic there is a relative change of 
0.00376 C. G. S. units of Force in the position of the datum 
planes of our two surveys. 

The direction of the slope is such as to indicate that the 

Vertical Force Disturbances deduced from our earlier survey were 

" - '" A ^e south and east and too small (algebraically) in the 

it. In our first memoir (p. 266) we drew attention 

> distribution of the vertical disturbances suggested 

of an error of this kind, and I returned to the 

other paper (Proc. Roy. Soc. Vol. 48, p. 532, 1890) 

:>re the observations had been made on which the 

I lines are based. It is therefore satisfactory to 



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THE MAGNETIC SURVEY OF GREAT BRITAIN 



117 



know that the correction introduced by the later observations is 
of the kind we anticipated. 

We decided to take the mean points between the two sets of lines 
when reduced to January i f 1 891, as the final terrestrial isomag- 
netics for that epoch. All the disturbing forces were recalculated, 
using these mean isomagnetics, and it is upon these that we base 
our description of the magnetic state of the United Kingdom. 

It must be remembered that it has already been shown that 
both surveys agree in their delineation of the principal magnetic 
features of the United Kingdom, and that therefore it is only in 
details that any inaccuracies can be introduced by combining 
them in this way. 

Nevertheless, we thought it desirable to investigate further 
whether there was in any district a residual error which might 
make the stations of either survey peculiar by relatively great 
Vertical Force Disturbances. The best way of putting this to 
the test appeared to be by a comparison of the Vertical Disturb- 
ances as deduced from the two sets of observations at each of 
the 25 repeat stations when referred to the mean terrestrial lines. 
If in any part of the country the average difference (taken with- 
out reference to sign) between the two values of the Vertical 
Disturbing Force exceeded the average error of experiment this 
fact would prove that errors were introduced by the method of 
treating the observations, and most probably by the reduction to 
a common epoch. 

To investigate this point it is necessary to determine what is 
the average difference between two absolutely independent 
measures of the Horizontal Force and Dip. 

In the account of our earlier Survey we showed that if the 
measurements ordinarily made in determining a single value of 
the Horizontal Force are divided into two independent groups, 
the probable divergence from the mean is ± 0.000028 (C.G.S.) 
giving a probable difference of ± 0.000056. 

In the later Survey the comparison was made in a less labori- 
ous way. Two measurements of the period of vibration were taken 
at the same station at different times. One of these was com- 
bined with the deflection, which was only measured once at each 
place ; from these observations the Horizontal Force and the 



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1 1 8 A . W. RUCKER [Vol. I, No. # 

moment of the magnet were then determined. The moments 
thus found during the whole of the summer were plotted, and a 
smooth curve drawn as nearly as possible through them. From 
this curve the value of the moment at each station was deduced 
and combined with the second vibration to calculate another 
value of the Horizontal Force. The conditions of the comparison 
being more varied the difference was greater than before, 
amounting to 0.00013. This is in good agreement with results 
obtained during the earlier Survey when, on eight occasions, we 
repeated the Horizontal Force observations at the same or at 
closely neighboring stations at intervals of less than two years. 
The probable difference was 0.00015, the mean difference being 
0.00017. When the interval between the experiments is greater 
than in these cases, so that the correction for secular change 
becomes more important; when they are made by different 
observers and the precise identity of the position occupied is 
more doubtful, and when different instruments are used (even 
though they have been carefully compared), or when the com- 
parison-correction to be applied to the instrument has altered 
appreciably, the error would be further increased. On the 
whole, then, we think that two absolutely independent measures 
of the Horizontal Force made five or six years apart and 
reduced to the same epoch would generally differ by 0.00020, 
that is by about 0.0012 of the whole value of the Horizontal 
Force in Great Britain. 

On this account alone the difference between the determina- 
tions of the Vertical Force would vary from 0.00050 in the 
south of England to 0.00060 in the north of Scotland, the mean 
being 0.00055. 

To this must be added the effect of errors in the Dips, and 
taking the difference of two measurements to be i\ the cor- 
responding difference in the tangent of the angle of Dip will be 
about one-thousandth part of its value. Hence the discordance 
. _ measures f the Vertical Force due to the Dip will be 
: 2.5 x 0.185 = 0.00045 in the south of England, and its 
; practically the same in the north. Combining the two 
ies 0.00055 an( * 0.00045 according to the law of errors we 
t the probable divergence of two measures of the Vertical 



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THE MAGNETIC SURVEY OF GREA T BRITAIN 1 1 9 

Force made under the specified conditions is : 

0.00005 X V 1 i a +9 3 = 0.00070. 
The mean of the differences of the two measures of Vertical 
Force made at 25 repeat stations at intervals of from four and 
one-half to eight years was 0.00066, so that they are completely 
accounted for by the errors of experiment, and by such irregu- 
larities of secular change as a comparison of the records of 
Greenwich and Kew reveals. It does not therefore appear that 
the results can be affected to any appreciable extent by residual 
errors of any kind. In each of the seven groups into which the 
25 stations are divided according to their geographical position, 
the mean difference taken with respect to sign is less, and in 
most cases very much less, than the mean taken when the sign 
is disregarded. This proves that there is no tendency for 
residual errors to accumulate in any part of the area of the 
Survey. 

It is probable that some magneticians may think that in the 
above discussion I have overestimated the errors of experiment, 
and it is true that the values given are much larger than those 
which are generally assigned to them. 

I must, therefore, once more insist on the great difference 
between the error of experiment when deduced from the results 
of observations taken consecutively on the same occasion, and 
when calculated from observations taken after an interval, when 
all the conditions are varied. 

The latter is so much larger that I cannot but think that the 
accuracy of the knowledge derived from magnetic surveys is 
often overestimated because, unlike ourselves, the observers 
have had no special reason for determining the magnetic ele- 
ments at any of their stations on two occasions separated by a 
considerable interval of time. The observations should be 
made with every precaution. To avoid difficulties due to acci- 
dental blunders and to test the accuracy of the work it is desir- 
able that at many of the stations each observation should be 
repeated twice on the same day. But when this has been done 
the error of experiment is so much less than that deduced from 
observations taken after a considerable interval with all the 
conditions varied, that multiplication of measurements on the 



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W" 



120 



A. W. RUCKER 



[Vol. I. No. 3] 



same day is of little^use except for some special purpose, such 
as the determination of the diurnal range. 

However this may be, it is satisfactory to record that the 
accuracy we attained was quite sufficient for our purpose. 

The range of the magnitude of the Vertical Disturbing 
Force in Great Britain, at places where the surface is comprised 
of sedimentary rocks, is about 0.00600 C. G. S. units. On 
granite and gneiss the range is doubled, and in the neighbor- 
hood of basalt it may be enormously increased. As, therefore, 
a single measurement does not on the average give a result cor- 
rect to within ±0.00033 C. G. S. units, we conclude that, 
although a doubt may sometimes arise as to the relative mag- 
netic levels of two stations, the mean levels of groups of sta- 
tions can be determined with adequate accuracy. No essential 
change which would alter to any important extent the positions 
of the principal ridge lines as shown on our maps would be pro- 
duced if the Vertical Force Disturbances were arbitrarily 
increased or diminished by 0.00033, even if the alterations were 
designed to produce the maximum change in the form of the 
lines. 

Turning next to the Horizontal Force Disturbances, we have 
not based any of our conclusions on the magnitude of these 
quantities, but we have made use of their directions to indicate 
the positions of the ridge and valley lines. By comparing the 
results obtained at the repeal stations we conclude that on the 
average our results as to the directions are correct to ± 9°.5 
when the two observations are referred to the two independent 
sets of terrestrial isomagnetics, but that this uncertainty is 
reduced to ±6°. 5 if they are both referred to the mean isomag- 
netics. 

It is evident, however, that no certain conclusions can be 
drawn as to the direction of the Disturbing Force unless the mag- 
nitude of the Disturbing Force is considerably greater than the 
error of experiment. We have therefore adopted 0.00030 C. G. 
S. units as the limit of the magnitude of the Horizontal Dis- 
turbing Force, below which the calculated value of its direction 
cannot be relied on. In the case of three of the repeat stations 
the force in question falls below this limit. At eight out of the 



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THE MA GNETIC SUE VEY OF GREA T BRITAIN 1 2 1 

remaining twenty-two stations the directions of the Horizontal 
Disturbing Forces, determined by observations made several 
years apart, are so nearly identical that we cannot depict them 
separately on the scale on which our maps are drawn. An 
inspection of the remaining fourteen pairs of directions is suffi- 
cient to show that our conclusions would not be affected if we 
were arbitrarily to reject either of the directions at any station. 

On the whole then this discussion of the data on which our 
conclusions are founded is sufficient to prove that the accuracy 
attained is amply adequate for the discovery and delineation of 
ridge and valley lines, and of magnetic districts in which Dis- 
turbing Forces tend toward fixed lines or centers. The remark- 
able agreement between the results obtained at neighboring 
stations, even when the Disturbing Forces are small, is also evi- 
dence that we have not underestimated any uncertainty which 
affects the data at our disposal. 

Having now investigated the accuracy with which the ter- 
restrial isomagnetics can be drawn and the Disturbing Forces 
determined, the next step in the development of our subject is 
to trace the ridge lines and determine the boundaries of the 
magnetic districts of which they are the central features. This 
cannot be done without frequent reference to a map, and in this 
brief summary I must avoid detail and confine myself to a gen- 
eral statement of our principal conclusions. To give some idea 
of the importance of the chief ridge lines I may state a few 
facts with regard to one of them which we have named the Lin- 
colnshire and Yorkshire line. (See Fig. i, p. 123, in which the 
arrows show the directions of the Horizontal Disturbing Forces.) 
We can trace its course without difficulty for 170 miles (say 270 
kilometers), and at both ends a connection is indicated (though 
less clearly) with other loci of magnetic attraction. At between 
fifty and sixty places the Horizontal Disturbing Force is 
directed towards the line, and ten points on the line, which 'are 
on the average about sixteen miles apart, are found to lie 
between pairs of places the average distance between which is 
twelve miles, so that the mean error does not exceed ±. 6 
miles. 

But in addition to lines which are thus clearly indicated both 



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1 22 A. W. RUCKER [Vol. I. No. 3] 

by the Vertical and Horizontal Disturbing Forces the more 
detailed Survey has enabled us to detect minor peculiarities 
which would have escaped notice in any less complete investi- 
gation. Thus it is often possible to follow for some distance a 
line of maximum Vertical Disturbing Force, on which the values 
of the Vertical Disturbances are either absolutely small or but 
little exceed those at neighboring stations. Such lines may 
exert comparatively little effect on the Horizontal Disturbing 
Forces, but they are often found to connect regions of high Ver- 
tical Force which woi Id otherwise appear entirely isolated, and to 
explain apparent anomalies in the directions of the Horizontal 
Forces. The magnetic phenomena which they exhibit are such 
as would be produced by vertical dyke-like sheets of magnetic 
matter, of which the horizontal thickness was small compared 
with either the horizontal length or the depth. Such vertical 
laminae would procj'ice greater effects upon the Vertical than 
upon the Horizontal Force. The two vertical faces would be 
oppositely magnetized, and would largely neutralize each other's 
effects. The lower horizontal face, being narrow and relatively 
distant, might be neglected. The upper horizontal face would, 
therefore, be the most important. For the purpose of illustra- 
tion let it be regarded as an infinite straight line at a depth d 
below the surface. The Vertical and Horizontal Disturbing 
Forces would be equal, and the latter would be a maximum at 
points on the surface at a distance d from that vertically above 
the line. Let them at that point be equal to 0.00030 C. G. S. 
units, 1. e., to the limit of the accurate determination of the 
direction of the Horizontal Disturbance. 

Under these conditions the Horizontal Disturbance would 
everywhere else be less than that limit, and thus the disturbing 
cause would not produce any clearly marked effect on the Hori- 
zontal Forces. On the other hand throughout a strip the 
breadth of which was equal to twice the depth of the disturbing 
line the Vertical Disturbance would vary between 0.00030 and 
0.00060 C. G. S. units. The larger of these quantities is nearly 
double, the smaller is about equal to the average error of the 
determinations of the Vertical Force Disturbance. 

Hence the effect of the line on the Vertical Force would he 



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THE MAGNETIC SURVEY OF GREAT BRITAIN 



123 



detected, while the Disturbance of the Horizontal Force would 
probably escape notice. This result would be still more likely 
to follow if the line ran through a region subject to other dis- 
turbances, due to more distant but more powerful centers of 
attraction. These might give to the Horizontal Forces direc- 
tions altogether independent of the minor ridge, the existence 
of which might nevertheless be traced by a clearly marked, 
though comparatively unimportant line of relative maxima of 
the Vertical Disturbances. Such lines may be regarded as sec- 
ondary ridge lines. They connect all the principal magnetic 
districts, and generally so clearly and simply that we cannot 
but believe that they are the less conspicuous parts of the mag- 
netic system, of which the more prominent features were discov- 
ered in our earlier work. 



Fiat. 



\ 



^ 



/ 



'/ 



\ 



\ 



\ 



\ 



S 



A 



\C 



iJVL 



LINCOLNSHIRE * ND 
YORKSHIRE DISTRICT. 



ncJUcs HAAbp/ XaaiAS .] 



^ 



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124 A. W. RUCKER [Vol. I. No. 3] 

Another advance which we have been able to make in one or 
;wo places is accomplished by investigating disturbances of the 
>econd order of magnitude 1 . If the whole of a relatively small 
urea is subject to the dominant influence of a widespread mag- 
letic disturbance, the forces due to which are nearly uniform 
:>ver the whole of the area, the effects of some more local cause 
nay be detected by a method of taking the differences from the 
nean values similar to that which we have applied to the coun- 
:ry as a whole. Thus the Cheviot Hills on the Scotch border 
ire composed of non-basic igneous rocks. To the north of 
:hem is a very powerful ridge line, and the Horizontal Disturb- 
ng Forces at all stations in the neighborhood of the Cheviots 
vith one exception (Kelso) are directed northwards. The 
nean northerly and westerly components of the force at the 
tight stations which surround but are clear of the igneous rocks 
ire 0.00038 and 0.00006 respectively. Subtracting these 
'egional forces from the corresponding components at the eight 
stations and at two others (Jedburgh and Kelso) which are 
:loser to the center of the disturbance we find that two places 
distant about 10 and 12 miles respectively from the crystalline 
rocks are not affected by their presence, but at the five stations 
which are nearest to the hills the purely local Horizontal Dis- 
turbing Force is directed towards them. At the remaining 
three places the directions of the forces are not towards the vis- 
ible igneous rocks, but they are so altered as to show that a 
minor ridge line runs through and to the west of them, thereby 
perhaps indicating an underground extension of the magnetic 
matter. Hence when the Disturbing Forces are cleared of the 
regional components they clearly indicate a feeble local attrac- 
tion due to the Cheviot Hills, and further make a suggestion of 
geological interest as to the conformation of the hidden rocks. 

1 Dr. van Rijckevorsel has independently adopted a similar plan in the discus- 
sion of his recent Magnetic Survey of Holland. 



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THE MA GNETIC SUR VEY OF GREA T BRITAIN 1 2 5 



PART III. 

ON THE RELATION BETWEEN THE MAGNETIC AND THE 

GEOLOGICAL CONSTITUTION OF GREAT 

BRITAIN AND IRELAND. 

In the memoir of which this paper is a brief summary we 
have carefully distinguished between the problem of determin- 
ing the positions of the loci and centers of magnetic disturb- 
ances, and that of explaining the means by which the Disturbing 
Forces are produced. On the latter point there may be some 
difference of opinion. 

The most probable causes of the Forces are electrical 
Earth currents and magnetic rocks, or both of these combined. 
It may be desirable to give an outline of the evidence which leads 
me to believe that the presence of magnetic rocks is the more 
potent of these sources of disturbance. 

Melton Mowbray in Leicestershire is the seat of a rather 
powerful local disturbance. The surface soil is non-magnetic, 
so that the situation is convenient for testing the Earth current 
theory. 

During our First Survey Mr. Preece, F. R. S., who was then 
chief Electrician to the General Post Office, was good enough to 
have measurements made of the potential differences between 
Melton Mowbray and several post offices at distances of from two 
to nine miles from that place. No relation whatever could be 
established between the direction of the Earth currents and that 
of the abnormal deviation of the magnet. Also the ratio of the 
potential difference per mile to the declination disturbance, 
when every assumption was made so as to favor the hypothesis 
under investigation was at Melton only 0.015 of the average 
value of the same quantity as determined at Greenwich from 
measurements made during twenty magnetic storms. As 
the direction of the Horizontal Disturbing Force at Melton is 
much altered within a mile and a half, and is reversed within 
seven miles, whereas in magnetic storms the effects produced 
are simultaneous over vast areas, the fact that the ratio of the 
supposed cause to the effect is some 66 times less in the case of 



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126 A. W. RUCKER [Vol. I. No. 3] 

the local disturbance than is that of the magnetic storms, though 
not conclusive, is certainly opposed to the view that the local 
disturbance is produced by Earth currents. 

Of course it may be urged that the currents may be deep 
seated, and cannot be detected by a measurement of the electro- 
motive forces which are measured close to the surface, but the 
fact that the direction of the Disturbing Force is completely 
altered within a few miles is not consistent with the suggestion 
that it is due to causes which emanate from very great depths. 

While, however, direct experiment fails to support the Earth 
current theory it does, on the other hand, prove that the mag- 
netization of hidden masses of rock by the induction of the 
Earth's field is sufficient to account for the observed facts, even 
if the concealed rocks are not more magnetic than the basalts 
and gabbros which are found on the surface. 

The main difficulties in measuring the magnetic properties of 
rocks are the facts that numerous specimens must be examined, 
as those gathered a few yards apart may differ considerably ; 
and that any method of determining the permeability which 
involves shaping the specimen to a particular form is practically 
inadmissible if large numbers are to be dealt with. 

To meet these requirements I devised the following scheme 
(Proc. Roy. Soc. Vol. 48, 1890). A series of standard magnetic 
fluids were made by suspending magnetic oxide of iron in vari- 
ous proportions of glycerine. The susceptibilities of these mix- 
tures were determined absolutely by the magnetometer method, 
and specimens of the rocks were compared with them by means 
of Professor Hughes' induction balance. For this purpose equal 
volumes of a mixture were placed in two similar test tubes, 
which were inserted in the cups of the balance, and the tele- 
phone was reduced to silence by means of a compensator. The 
rock to be tested was now immersed in one of the mixtures, and 
lume of the liquid having been abstracted, the zero 
mined. Two mixtures were thus found, to the sus- 
of which that of the rock under experiment was 
e, and from these the susceptibility of the rock could 
:d by the method of proportional parts, 
number of specimens of basalt and gabbro were 



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THE MAGNETIC SURVEY OF GREAT BRITAIN 1 27 

placed at my disposal by my colleague Professor Judd, F. R. S. 
The average magnetic susceptibility of all the specimens from 
the west of Scotland and from Ireland was 0.00245, that of the 
specimens from Mull was 0.0016. I have since examined 
samples of Australian rocks with very similar results. {Pro. 
Roy. Soc. New South Wales, June 6, 1894, p. 51). 

Having thus obtained some knowledge of the average mag- 
netic properties of basic rocks it was easy to calculate the Dis- 
turbing Forces which the presence of such rocks would produce 
if they were magnetized by induction in the Earth's field. I 
assumed that at a depth of 12 miles (20 kilometers) the tem- 
perature would be so great that magnetite would lose its mag- 
netic properties, and compared the forces due to large slabs of 
basalt of a thickness less than this depth, with the mean Disturb- 
ing Forces observed on the surface. 

The permeability of the magnetic rocks being very small each 
side of a rectangular mass will be uniformly magnetized, and the 
problem of finding the magnetic forces is reduced to that of 
rinding the resultant forces exercised by rectangular plates of 
attracting or repelling matter of constant density (<r). 

If k is the susceptibility of the material and F is the Earth's 
field resolved perpendicular to the plate, <r=*F. 

The forces may be expressed in various ways. The formulae 
I have usually employed are as follows : Through a point P let 
planes be drawn perpendicular to the plate and parallel to its 
edges. Let the points on which these meet the edges of the 
rectangle or the edges produced be joined to the point, and let 
these lines make angles <£ a "and <f> lt a and 6 t with the normal. 

Then the component perpendicular to the plate is 

tr {sin -I (sin<ksin0 a ) — sin -1 (sin<ksin0,) — sin" 1 (sin<k sin0 a ) 

-f sin "" ' (sin <k sin t ) \ • 

The component parallel to the plate and to the plane of the 
<*>'s is 

u ) *°ge ( cos< k sin 0»+ -J 1 — sin a a sin a <k) — log e (cos<£ a sin0 a 
+ Ji — sin 9 a sin a <k) — log e (cos <ksin0 t + J 1 — sin 8 *, sin a <£ x ) 

+ log c (cos <f> 3 sin t + ^1 1 — sin a t sin 9 <£ a ) | * 



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1 28 A. W. RUCKER [vol. I, No. 3] 

The component parallel to the plate and to the plane of the 
0's is obtained from the last by writing <f> for 6 and vice versa. 

For the details of the calculations I must refer to the original 
paper. It is perhaps sufficient to say that it is there proved it is 
quite possible to imagine a distribution of magnetic matter at 
depths between 135 meters and 20 kilometers, and of no greater 
permeability than the Mull basalt, the mere presence of which 
in the Earth's magnetic field would produce Vertical Disturbing 
Forces of the same order of magnitude as those actually 
observed in Great Britain and Ireland, and Horizontal Disturb- 
ing Forces rather larger than those given by experiment. 

Similar calculations have been applied to a number of special 
cases with results which are always conformable to the theory. 1 

The magnetic rock theory is unquestionably open to the 
criticism that whereas it attributes Disturbances which extend 
for scores or even hundreds of miles to magnetic rocks, large 
masses of such rocks often produce little or no effect at what are 
regarded as surprisingly small distances. 

It is therefore desirable to show that results, which are at 
first sight discordant, do not in any way invalidate the hypoth- 
esis. Some of them can hardly be said to support it, as the 
bases of the magnetic masses are concealed underground, and in 
the calculations, assumptions which are unproved and are per- 
haps incapable of proof, have to be made as to the forms of 
these concealed foundations. All that can be done is to show 
that the different results are compatible with, and are therefore 
not valid evidence against the rock, theory. 

The discussion may be divided into five heads, viz., the rela- 
tions of magnetic ridge lines or centers of attraction to : 

( 1 ) Dykes, basaltic sheets, and isolated masses of trap the 
largest linear dimensions of which do not exceed a mile or two. 

(2) Districts which are either entirely basaltic or in which 
numerous masses of trap appear. 

(3) Non-basic masses of igneous rock. 

(4) Faults. 

(5) Regions in which the arrangement of the rocks is anti- 
clinal. 

1 In the remainder of this paper there are large quotations from the original memoir. 



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THE MA GNETIC SURVEY OF GREA T BRITAIN 1 29 

As to vertical dykes or horizontal sheets of basalt the thick- 
ness of which is small when compared with their other dimen- 
sions, it is easy to show that the Disturbing Forces would be 
largest close to the edge. The opposite sides of such a magnetic 
plate would be oppositely magnetized, and the forces would be 
almost exactly balanced unless the distance from the edge is a 
small multiple of the thickness. 

Thus even if the outcrops of the dykes and sheets were infi- 
nitely long, and if the vertical dimensions of a vertical dyke, and 
the horizontal extension of a horizontal sheet were infinite, their 
magnetization by the Earth's field could not produce disturbing 
forces which could be detected at a distance from their edges 
equal to six times their thickness unless they were much more 
magnetic than basalt ordinarily is. 

These considerations may be applied to explain the small 
magnetic effects of relatively large groups of basic rocks. 

For this purpose it is convenient to exhibit in a table the 
Forces due to a rectangular mass of basalt, of which the top and 
bottom surfaces are squares and the sides are vertical, when it is 
magnetized by the Earth's magnetic field in the United King- 
dom. 

We will suppose the mass to be so arranged that two sides 
are in the magnetic meridian. The other two are, therefore, 
magnetized by the horizontal component of the Earth's field. 

The point, for which the Disturbances are calculated, is in 
the vertical plane which bisects these two sides, and in the plane 
of the upper surface. All lengths are expressed in terms of that 
of a horizontal side of the parallelopipedon. 

The Forces are calculated for the two susceptibilities 0.0016 
and 0.0024, and are taken as positive when directed toward the 
basaltic mass. 

The Disturbances are in term of 0.00001 C. G. S., i. e. f 0.0001 
metric units. The results are as follows : 



Depth 
edge 


Distance 
from near- 
est face 


Horizontal Disturbance 
#c = 0.0016 « = 0.0034 




I 

X 

I 


13 or— I 

51 or 9 

5 or —2 

24 or —3 


18 or — 2 

76 or 13 

7 or —3 

36 or —5 



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1 30 A. W. RUCKER [vol. i. No. 3] 

The values given in each case are for corresponding positions 
on opposite sides of the mass. The Forces due to the hori- 
zontal faces are in each case the same, but those produced by 
the vertical faces change sign according as the point is mag- 
netic north or south of the rock. 

If we suppose that instead of being vertical the nearer face 
of the rock has a slope of 1 in 8, the Forces at distant points are 
increased. One example will suffice. 

Depth Distance 

edge from near- Horizontal Disturbance 

est face 

It is evident from the first set of figures that the Forces at 
distances such as those for which the calculations are made, 
diminish very rapidly with the vertical thickness of the plate. 

Thus, if a mass of basalt, a mile and a half square, of sus- 
ceptibility 0.0024, were three-eighths of a mile, 1. e. % say 2000 
feet thick, the Horizontal Disturbance a mile and a half from it 
would be quite negligible, amounting to only 0.00007 C. G. S. 
units towards the rock on one side, and 0.00003 away from it on 
the other. 

If the susceptibility were not greater than that of the Mull 
specimens, the columnar mass might be 4000 feet deep, and yet 
produce at points a mile and a half distant Horizontal Disturb- 
ances far below our limit of the accurate determination of direc- 
tion. It will be remembered that this limit is 0.00030 C. G. S. 
units, whereas the forces in question are 0.00013 and 0.0000 1 
units respectively. 

These calculations throw light upon observations made near 
Titterstone Hill in Shropshire, as they explain a negative result 
obtained near to it. The hill consists of two masses of basalt, 
of which the larger is about two miles long and one mile wide. 

Basaltic pipes or feeders may extend downwards to an indefi- 
nite depth, but the sheet is of small thickness and has been 
pierced by the shafts of coal mines. 

It is immediately surrounded by a narrow band of the coal 
measures, which are succeeded by the Old Red Sandstone. 

Observations were made on the east and west sides at Bit- 



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THE MA GNETIC SURVEY OF GREA T BRITAIN 1 3 1 

terley and Hopton Wafers, at points about a mile and a half 
from the basalt. 

The result was that the Horizonal Disturbing Force at Bit- 
terley acted nearly due west, i. e., at right angles to the line 
joining the station to the center of the basalt. Hence, no rela- 
tion whatever was established between the directions of the Dis- 
turbing Forces and the magnetic rocks. 

This result is in conformity with the above calculations, but 
it may be observed it has more than a merely negative value. 
If a relatively thin sheet of basalt were extruded through pipes 
communicating with a deep-seated magma, it is conceivable that 
in some cases the position of the outflow might have been deter- 
mined by the nearer approach of the magma to the surface. 

If this were the case, and if the top of the concealed under- 
ground basaltic fold were at a moderate depth, it is possible that 
attractions in play in the neighborhood of the visible magnetic 
mass, which could not be due to it, might be caused by its con- 
cealed foundations. Thus the absence of attractive forces a 
mile and a half from Titterstone Hill proves that there is beneath 
it no very remarkable pillar-like prominence on the basic sub- 
stratum. 

Conclusions such as these are important, a showing that even 
within moderate distances of relatively large masses of basalt 
the regional forces may be determined free from all purely local 
disturbance. 

BASALTIC DISTRICTS. 

We now turn to the apparently inconsistent deduction that, 
in spite of this fact, magnetic rocks may account for ridge lines, 
which appear to dominate very large areas. 

In such cases we have to assume (i) that the vertical thick- 
ness of the mass is much greater than has hitherto been supposed, 
and (2) that it extends laterally underground to great distances 
from the points where it occurs on the surface. 

These assumptions must, we think, appear reasonable, though 
in some cases, no known geological facts may warrant them. 

It must, however, be remembered that the knowledge of geolo- 
gists is practically confined to a few thousand feet from the sur* 
face, and in many cases does not extend so far. 



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I 32 A. IV. RUCKER [vol. I, No. 3] 

But the magnet would be capable of detecting large masses 
of magnetic rock at a depth of several miles, and the theory we 
are discussing can hardly be entertained unless we can assume 
that such masses exist. 

Nor is the hypothesis of the lateral extension of trap rocks 
for great distances around the points where they appear on the 
surface negatived by the fact that the sides of the visible mass 
are vertical, or that it is known to be a relatively thin sheet. 
The surface basalt may spring from a great underground fold of 
magnetic matter, which may slope gradually away from the area 
at which more or less accidental circumstances determine the 
form of the extruded mass. 

If, however, this is so, we must draw attention to the fact 
that these considerations reduce the significance of the particular 
place or places where the rocks appear. The highest point on an 
island may be at one end. Mountain chains do not culmi- 
nate exactly at their centers. In like manner the point at which 
an underground mass of basalt reaches the surface may or may 
not lie on the magnetic ridge line which marks the points where 
the downward pull due to the whole mass is a maximum. This 
might explain the fact that near Limerick, and in several other 
places, masses of basalt lie near to but not on a ridge line. 

If, on the other hand, the exposed portion is very large and 
widespread, its relative importance must be greater, and it is 
more likely that it will be closely associated with a locus of 
attraction. In this case, however, difficulties of an opposite kind 
are encountered ; the local disturbances being so great that, 
although ridge lines may be traced up to the mass, it is difficult 
to follow them across it. 

All therefore that can be expected is that we should be able 
to show that far-reaching underground extensions of basaltic 
rocks would be competent to produce the observed disturbances, 
and that in the case of very large exposures of basaltic rocks 
the regions in which they occur are in general clearly marked 
centers of attraction. 

We will take these points in order. The first has been dealt 
with in the paper already referred to, but the application of cal 
culation to the case of Antrim will serve as an additional example. 



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THE MAGNETIC SURVEY OF GREAT BRITAIN 1 33 

The basaltic surface of Northeast Ireland may be roughly 
represented by a square, each side of which is 50 miles long. The 
length from north to south is somewhat greater, and the breadth 
less than 50 miles. It forms the center of a magnetic district 
which extends some 50 miles from the edge of the basalt. 

The calculations referred to above are not applicable when 
the distance involved are so great that the curvature of the Earth 
has to be taken into account. In this case, however, they are 
sufficiently accurate to illustrate the principle. 

The thickness of the Antrim basalt after denudation is only 
about 1 200 feet. Disturbances directly due to the visible mass 
would therefore be unimportant a very few miles from its edge. 

Even if we supposed the basalt to extend from the surface 
to the depth at which it would cease to be magnetic (say 12 
miles) the ratio of the thickness of the block to the length of 
an edge would not exceed one-fourth, and it has been shown 
that such a mass would produce no effect at a distance from the 
nearest face equal to the length of an edge, that is, at 50 miles, 
whereas at Letterkenny and Stranorlar, which are about 40 
miles distant, the attractive Forces, though not large, are 
appreciable. 

We can explain, therefore, the Forces at these places by their 
proximity to Antrim only on the assumption that beneath the 
basaltic district there is a magnetic mass, the upper face of which 
is separated from, but approaches relatively near to the visible 
mass (say, within a mile or a mile and a half) and slopes away 
from it towards the west. 

It would then approximately fulfill the conditions assumed by 
the second calculation given above. Its upper surface would be 
six miles below the sea level at 50 miles from the edge of the 
visible basalt, but the Horizontal Force would be 0.00036 instead 
of only 0.00007 C. G. S. units. As a matter of fact, the Hori- 
zontal Disturbance at Letterkenny is 0.00035, anc * at Stranorlar 
0.00041 C. G. S. units. The close agreement between these 
numbers and the calculated Force is, of course, accidental but 
they are sufficient to show that, although masses with steep sides 
and of moderate thickness would present very small Forces at 
distances from these edges comparable with their linear dimen- 



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134 



A. W. RUCKER 



I Vol. I. No. 3] 



sions, yet if the sides slope gradually away the Forces may be 
appreciable. 

It must also be remembered that although the highest suscep- 
tibility we have taken as a basis of calculation is the mean of a 
number of specimens from Scotland, much larger mean values 
were obtained in groups of specimens from Skye. All the largest 
values of the Forces above calculated might be doubled without 
the susceptibility exceeding that of rocks which occur on the 
surface, and, even if in any given locality the surface rocks are 
only feebly susceptible, it is possible that they may overlie more 
strongly magnetic masses. 

On the whole, then, it appears that all the observed facts, the 
smallness of the Disturbances in some cases, and their magnitude 
in others, are consistent with the theory that they are caused — 
in part, at all events — by basic rocks magnetized in the Earth's 
field. 

We now proceed to inquire how far the main centers in 
which basic rocks occur are also centers of magnetic attraction. 

The easiest way of conducting the inquiry is to study stations 
near the main masses of igneous rocks, but yet sufficiently dis- 
tant to make local Disturbances unimportant as compared with 
the regional attraction. 

If at all such stations the Horizontal Disturbing Forces tend 
towards the igneous mass, it is obvious that it is on the whole a 
center of attraction. 

Of course doubtful points arise, in deciding which there is 
sometimes room for difference of opinion. 

Thus if a comparatively insignificant group of magnetic rocks 
appears on the surface, near to, but completely detached from, 
a much larger intrusive mass, it may be doubtful whether it 
should or should not be included within the girdle of external 
stations. 

If it is included, it may divert the line so far from the central 
region, that the cogency of the proof is diminished. If it is not 
included, there is the risk that, though of trifling superficial 
area, it may represent an important underground extension, and 
that the Disturbing Forces in the intermediate space may be sub- 
ject to local variations. 



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THE MA GNETIC SURVEY OF GREA T BRITAIN 1 3 5 

On the whole we have thought it best in each case to keep 
as near to the principal mass of rock as possible, but if the dis- 
trict between it and an apparent outlier appears to be locally 
disturbed, we have carried the boundary outside the latter. In all 
cases, where any doubt can arise, the reasons for the selection 
of the stations are given. 

Another difficulty arises from the fact that the disturbances 
due to igneous rocks, which appear on the surface, are interfered 
with by important ridge lines, which are either connected with 
another group of rocks or traverse a neighboring district where 
the superficial soil is non-magnetic. 

Obviously all difficulties are increased if a magnetic district is 
largely covered by the sea. 

There are three principal districts in which basic rocks are 
found, with a profusion far exceeding that which occurs in any 
other part of .the United Kingdom. They are Antrim, Mid- 
Scotland, and the West Coast of Scotland. 

The first two of these unquestionably attract the needle at 
places near to but clear of the magnetic rocks. 

To prove this we need only refer to our maps, in which the 
basic rocks are indicated, and the directions of the Horizontal 
Disturbing Forces at stations near the rocks are shown. 

All round the Antrim basalt the Horizontal Disturbing Forces 
are directed towards it. This is shown at no less than fourteen 
places, viz., Drumsurn, Dungiven, Sperrin, Dungannon, Armagh, 
Lurgan, Lisburn, Belfast, Carrickfergus, Lame, Ballygalley Head, 
Carnlough, Waterfoot, and Ballycastle. Gortin and Omagh are 
too far from the basalt to be described as near it, but they serve 
to complete the chain of stations. (See Fig. 2, next page.) 

At Draperstown the Horizontal Disturbance is directed away 
from the basalt, in which, however, this station is to a certain 
extent embayed. It therefore hardly satisfies the condition we 
are laying down ; viz., that the stations considered must be clear 
of the attracting mass. 

Similarly, a line of stations can be drawn round the Scotch 
Coal Field District, which indicate that it, too, is a center of 
attraction. They are Campbelton, Torrisdale, Loch Ranza, Cum- 
brae, Row, Dunblane, Crieff Junction, Perth, Stanley Junction, 



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136 



A. W. RUCKER 



[Vol. I, No. 3J 



Glamis, St. Andrews, Dunbar, Heriot, Dolphinton, Carstairs, 
Abington, Loch Doon, Pinvalley, and Penwherry. (See Fig. 3, 
opposite.) 



kJh*, Xx>V^oruta£. D^JKujiAa*^ Sottot , 3 






On the West Coast there is not the same clear evidence that 
the visible masses are centers of attraction. We have shown in 
our original memoir that the hypothesis that ridge lines run 
through Skye and Mull is consistent with the facts, but the 
effects of the visible masses appear to be of less importance 



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THE MAGNETIC SURVEY OF GREA T BRITAIN 1 37 

than those due to concealed centers. In Skye there is a power- 
ful focus of attraction on the eastern portion of the island, where 
the surface rock is not basalt ; and, the effect produced by Mull 



is subordinate to an attraction directed to a submarine center to 
the south of the Hebrides. *V 

The facts that much of this district is covered by the sea, 
and that important ridge lines which run near its boundaries 
make it very difficult to solve all the problems it suggests should, 
however, be borne in mind. 



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I 38 A. W. RUOCER [vol. i, No. 3] 

It is impossible in this summary to illustrate the other mag- 
netic districts as fully as Antrim and Scotland, but the accom- 
panying map (Fig. 4) may help to elucidate the rest. The dark 
lines represent the magnetic ridge lines or loci of attraction. 
The lines are drawn full when the positions of the ridge lines are 
clearly indicated, dotted when they are more doubtful. The 
thin lines represent the magnetic valley lines. The letters B B 
indicate a district on which a large area is covered by basalt; 
B a district in which the masses are smaller but still important. 
The letter b indicates a still smaller mass, and a line of small 
masses is shown by a row of b's. The names of the most impor- 
tant places, and some references to the geological state are also 
inserted. With the aid of this map I trust that what follows 
may be intelligible. 

Next to the districts above mentioned, North Wales is, per- 
haps, that in which the largest basic masses occur. This is 
unmistakably a center of attraction. The Horizontal Disturbing 
Forces at Beaumaris, Carnarvon, Pwllheli, Port Madoc, Aber- 
gwynolwyn, Bala, Bettws-y-Coed, and Llandudno are all directed 
towards the igneous rocks, which are in part basic, and may in 
part rest on a basic substratum. 

Following next in importance after North Wales come Devon- 
shire and Cornwall, Wexford and Wicklow. In both of these 
the basic masses occur in long lines, which suggest that they 
have not much lateral extension, or that they are the edges of 
relatively thin sheets, or are connected with narrow pipes. How- 
ever this may be, though there are suggestions of lines of mag- 
netic attraction parallel to both of them, in Devonshire and in 
the east of Wexford, neither is a center of attraction. There is 
a station of relatively high Vertical Force on the serpentine of 
the Lizard, but here, too, the main center of attraction appears 
to be out at sea. 

Three other districts remain. The most important is North- 
West Donegal, a wild region, in which we have comparatively 
few stations. At five stations near Londonderry the Horizontal 
Disturbing Force is directed towards the trap rocks. The same 
statement is true of the stations to the north of the basic masses 
near Newry and Carlingford in Down. To the south of these 



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140 A. W. RUCKER [Vol. I, No. 3] 

the main attraction is exerted towards a ridge line which runs 
out from them, and probably marks an underground continuation 
of the trap. 

In Pembrokeshire, also, the strips of igneous rocks lie close 
to a ridge line, and the horizontal disturbing forces at Cardigan, 
Haverfordwest and Milford are directed towards it. 

The basalt to the southeast of Limerick also lies near a ridge 
line but is not a center of attraction, though some of the igneous 
rocks are very basic. 

The scattered masses in Mid- Wales and Mid-England, and 
the dykes in the north of England, have to be discussed separ- 
ately. 

Putting them aside, the results we have arrived at may be 
summed up as in the following table : 

PRINCIPAL MASSES OF TRAP ROCKS IN THE ORDER OF THEIR 
IMPORTANCE. 

Skye and Mull - Probably traversed by ridge lines. 

Antrim - - A center of attraction. 

Mid-Scotland - - A center of attraction. 

North Wales - - A center of attraction. 

Wexford and Wicklow No apparent regional magnetic 

effect. 
Devonshire and Cornwall No apparent regional magnetic 

effect (except at the Lizard). 
Donegal - - A center of attraction. 

Pembrokeshire - On a ridge line. 

Limerick - - - Near a ridge line. 

IGNEOUS ROCKS WHICH ARE BUT SLIGHTLY, OR NOT AT ALL BASIC 

In general, masses of non-basic igneous rocks appear to pro- 
duce little or no effect on the needle. This holds good of Dart- 
moor, Wicklow, and many parts of Scotland. Exception to this 
rule are found in the Cheviots and in Galway. 

The attractions apparently exerted in these cases by rocks, 
which, taken as a whole, are but feebly magnetic, are, we believe 
:apable of an explanation quite in accord with the recent ten- 
dency of opinion among geologists. It is thought that in many 
:ases the fluid magma out of which the rocks were formed was 
irranged in layers of various densities, the lighter non-basic 



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THE MA GNETIC SUR VEY OF GREA T BRITAIN 1 4 I 

materials floating on the heavier and more magnetic constituents. 
Where such a separation occurred a group of non-susceptible 
rocks would now stand upon a magnetic foundation. It is con- 
ceivable that investigations, such as our own, may help to deter- 
mine where this is the case. 

FAULTS. 

It appears at first sight that the magnet would be affected if 
a fault in the superficial strata extends down to magnetic 
rocks. 

There are, however, a number of arguments which show that 
no noticeable disturbance might be produced. 

If the depth at which the magnetic rocks occur is, say, four 
or five times the throw of the fault, the magnetic effects would 
in general be very small. 

Even when this is not the case, the possible effects are more 
complicated than would at first be supposed. If the magnetic 
rocks form a horizontal slab, the Vertical Force due to the hori- 
zontal faces will be positive above the mass, but negative at parts 
near to but not over it. The positive or negative Forces may be 
strengthened or may not be affected by the vertical face, accord- 
ing as the latter is perpendicular to the magnetic meridian and 
to the south of the slab, or in the magnetic meridian. 

The Horizontal Disturbing Forces in such a case will not be 
directed to the fault, but to the center of the mass of which it 
marks the boundary. 

According to Sir Archibald Geikie, however {Encycl. Brit., 
Ed. IX, Vol. 10, p. 261), a fault or dislocation is nearly always 
inclined to the vertical. 

If the basaltic slab, which is assumed to underlie it, were not 
horizontal, the effects of the fault itself would be interfered with 
and masked by the disturbances due to the approach of the mass 
towards the surface. 

There is, therefore, no a priori reason for supposing that a 
fault must coincide with a line of attraction. 

If it does, it will be rather a proof of a favorable conforma- 
tion of hidden magnetic rocks than an illustration of a general 
principle. Thus, two stations at Bewdley on either side of the 



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I 42 A. W. RUCKER [Vor. I. No. 3] 

well-known fault, which runs from that place towards Malvern 
do not appear to be affected by it. 

In Scotland and the North of Ireland, however, some of the 
magnetic ridge lines, if not coincident with, are for some distance 
parallel to important faults. This is true of the Great Glen 
(Caledonian Canal), of the South Highland fault which crosses 
Scotland from the Clyde to Stonehaven 1 and of the fault which 
runs southwest from Antrim. 

The magnetic observations tend to show that the fault line 
of the Great Glen is prolonged northwards, but, on the other 
hand, the extension of the fault southwards by Lock Swilly to 
Donegal Bay is not indicated by the magnet, or is masked by 
the neighborhood of the Antrim and Donegal basic rocks. 

A magnetic ridge line runs close to the South Highland fault 
for about sixty miles. It appears, however, to cross it near its 
northern boundary and does not follow its promulgation south- 
west towards Donegal Bay. 

The Galloway ridge line runs for some distance nearly paral- 
lel to, though at an average distance of some twenty miles from, 
the fault which bounds the Mid-Scotland district on the south. 
For the rest, there does not seem to be any very close connec- 
tion between the geology of Scotland and the other magnetic 
ridge lines in that country. 

REGIONS OF UPHEAVAL. 

If it be true that magnetic ridge lines sometimes indicate the 
physical ridge lines of underground magnetic masses, it seems 
probable that there would be a connection between them and an 
anticlinal arrangement of the surface strata. It is fevident, how- 
ever, that in this case, also, it is difficult to decide upon what we 
ought a priori to expect. 

No one, whose knowledge of the geology of the London basin 
was confined to the surface only, would suspect the existence 
of the Palaeozoic ridge upon which it rests. It is quite possible 
that similar elevations of the assumed deep lying magnetic rocks 
may be unsuspected by geologists, but may be detected through 
all the intervening strata by the magnet. 

1 This fact has been established by our later observations. See " Mem. 90," p. 318* 



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THE MAGNETIC SURVEY OF GREAT BRITAIN 143 

Again, in Mid-Scotland and elsewhere, vast masses of basalt 
on the surface are associated with rocks newer than those which 
bound them both to the north and south. If the newer rocks 
hid the basalt a magnetic ridge line would appear to be associ- 
ated with a synclinal axis. Anomalies are, therefore, to be 
expected, and we propose to bring together the cases in which 
our results, when interpreted on the magnetic rock theory, are 
in accord or in disagreement with surface indications, not so 
much with the intention of supporting the view to which, on the 
whole, we incline, as of collecting in a convenient form the argu- 
ments which may be adduced for or against it. 

The magnetic indications appear to be quite independent of 
the disposition of the newer strata. 

The Weald of Kent is a region of geological upheaval, but 
of low Vertical Magnetic Force. On the other hand, a magnetic 
ridge line runs across the geological depressions in North York- 
shire. 

Again: The well-marked ridge line which runs from near 
Reading to Chichester, has no apparent connection with the 
superficial geology. 

Among the more ancient rocks the lower Carboniferous strata 
in Devonshire lie between the older Silurian and Devonian forma- 
tions, but a ridge line traverses them right across the county. 

This is, however, almost the only exception, in England and 
Wales, to the rule that in the case of rocks older than the Coal 
Measures there is an approximate agreement between regions of 
geological upheaval and of high Magnetic Vertical Force. 

This is true of the Mendip Hills. 

The line which runs through South Wales and Gloucester- 
shire towards Reading, ranges from Pembrokeshire, where the 
older Palaeozoic rocks are mingled with trap, through a region in 
which the Palaeozoic rocks are probably not far below the sur- 
face. 

It may mark a line along which the older Palaeozoics are 
ranged, though covered unconformably by newer Palaeozoic rocks. 

The line in Mid-Wales and Shropshire is for some miles par- 
allel to the fault which runs from the Wrekin to Radnor. It 
starts where the Builth igneous rocks are exposed, runs by Wen- 



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144 A. W. RUCKER [Vol. I, No. 3] 

lock Edge and the Wrekin — where again there is a mass of 
trap — and then passes direct from the older rocks in this neigh- 
borhood towards those of Derbyshire. It certainly suggests an 
underground connection between them. 

Another ridge line connects the Nuneaton and Dudley Coal 
Fields which rise in the midst of newer rocks. The southward 
prolongation of this line towards Reading does not correspond 
with any surface indications. A slightly marked line, which is 
probably connected with this, runs northeast from Lichfield to 
Nottingham, passing through the patch of older rocks which 
occurs to the north of Charnwood Forest. 

To the east of Reading the more southerly of the two ridge 
lines coincides roughly with the line of the Palaeozoic ridge, but 
it is rather to the south of the points in which the oldest rocks 
probably approach nearest to the surface. The more northerly 
line passes through Ware, near which Silurian rocks have been 
proved. In the north of England the magnet is attracted to a 
line which roughly follows the axis of greatest geological eleva- 
tion from the lake district to Harrogate, and thence southwards 
through Derbyshire. A branch traverses the Lancashire coal 
field, which projects like a promontory among later formations. 

This concludes the evidence that there is a certain though 
somewhat loose connection between ridge lines in England and 
regions of upheaval of the older rocks. 

The Derbyshire and the Yorkshire magnetic ridges are obvi- 
ously prolonged under the newer strata in the East Midland and 
eastern counties. The latter line especially passes close to Mar- 
ket Weighton where the Jurassic rocks thin out, and which was 
recommended as a station by Professor Judd on account of the 
probability of the older rocks approaching the surface there. In 
Southeast Lincolnshire folds in the new strata have recently been 
discovered, which run parallel to our ridge line, and may be con- 
nected with more deeply-seated undulations. 

In Scotland the magnetic lines appear to be chiefly associ- 
ated with the basaltic masses and the faults. These have been 
already discussed. 

In Ireland a ridge line is associated with a succession of 
Silurian masses, which lie between newer rocks and are marked 



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THE MA GNETIC SUR VEY OF GREA T BRITAIN 1 4 5 

by the Galtee, Silvermine and Slieve Bloom Mountains respec- 
tively. 

It is connected with a slightly marked ridge line, which 
appears to be a continuation of the Palaeozoic ridge, and with 
others which run to the igneous rocks of Connemara and of 
South Down. From Connemara the ridge is continued north- 
east parallel to the Silurian ridges and to the faults which occur 
in this part of the country. 

On the whole then it appears that the connection between 
the magnetic ridge lines and the geological conformation of the 
country, though in some cases clearly suggested is only such as 
would follow if the magnetic effects were due to deep-seated 
folds in the magnetic rocks, which are not always directly con- 
nected with the arrangement of the surface rocks. 

The general results may be summed up as follows : 

( 1 ) Theory leads us to expect, and experiment shows that 
dykes and thin basaltic sheets produce no measurable Disturb- 
ances at distances which are small multiples of their thickness. 

(2) Theory leads us to expect, and experiment shows that 
masses of trap rock, a few square miles in area, produce no 
noticeable magnetic effects at distances comparable with their 
linear dimensions. 

(3) Theory leads us to expect that the effects of faults 
would be irregular. They would only correspond to ridge lines 
in special cases. There may be large positive or negative Verti- 
cal Forces in their neighborhood. If the fault is inclined at a 
considerable angle to the vertical, or if the depth of the mag- 
netic rocks is four or five times the throw, little or no effect 
will be produced. 

Experiment shows that ridge lines are certainly associated 
with the great faults in Scotland and with a fault in Ireland, but 
that there is no clear connection between them elsewhere. 

(4) Large masses of basalt such as those which occur in 
Skye, Mull, Antrim, the Scotch Coal Field, and North Wales, are 
always centers of attraction. 

(5) Non-basic igneous rocks often produce little or no effect, 
but sometimes, and notably in the cases of Connemara and of 



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146 A. W. RUCKER [Vol. I, No. 3] 

the Cheviots and Berwickshire District they are centers of attrac- 
tion. In both these regions basic rocks occur. 

(6) In no case does a large igneous mass repel the north 
pole of the needle. The only case in which the suspicion of such 
repulsion could arise is that of the Wicklow Mountains, and the 
facts would there be equally well explained by supposing the 
magnetic effects of the granite to be negligible. 

(7) The magnetic ridge lines often occur in districts where 
there are no magnetic rocks on the surface. They appear to be 
unaffected by the distribution of surface rocks of later date than 
the Coal Measures, but there are a number of cases in which they 
are associated with an anticlinal arrangement of the older rocks. 
To this the lower Carboniferous formation of Devonshire is an 
exception. 

The sixth of these conclusions is of great theoretical impor- 
tance. If the rocks are magnetized by induction they would 
attract the north pole of the needle. If they merely deflected 
earth currents, there seems to be no reason why the eddies thus 
produced should always circulate in the same direction, which 
would be necessary if they were the cause of the attraction which 
is always in play in the neighborhood of the rocks. 

The fact that the general result of magnetization of the rocks 
is to attract the north pole of the needle is not inconsistent with 
the observation that close to the basalt the magnetic forces are 
very irregular being alternately attractions and repulsions. These 
effects are due to permanent magnetization, the distribution 
of which appears to defy forecast. At a distance these antag- 
onistic forces neutralize each other, while those due to the less 
powerful but more uniform effects of induction become predomi- 
nant. 

In conclusion I may add that the description of the results 
of our work, which I have just given, is largely quoted from the 
original memoir, and that I cannot but feel that the full signifi- 
cance of the facts will be imperfectly comprehended without the 
aid of the large maps with which that memoir is illustrated. 



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DIE MAGNETISCHEN STORUNGEN DER JAHRE 1890-95, NACH 

DEN AUFZEICHNUNGEN DES MAGNETOGRAPHEN 

IN POTSDAM. 

Von Dr. G. Ludeling in Potsdam. 

In den "Ergebnissen der magnetischen Beobachtungen in Potsdam in 
den Jahren 1890 und 1891 " (VerbffentL des Kgl. Preuss. Meteorolog. Institute, 
Berlin 1894) giebt Herr Eschenhagen eine Classification der magnetischen 
Curven, nach welcher er 5 verschiedene Arten unterscheidet, und zwar 
bezeichnet er mit 

Character 1 : Sehr ruhige Curven, die hochstens vereinzelte, sehr kleine 
Ausbuchtungen zeigen ; 

Character 2: Curven mit ziemlich ruhigem Verlauf ; das Gesammtbild 
der taglichen Periode wird durch etwas haufigere, kleine Wellen nicht beein- 
trachtigt ; 

Character 3: Leicht gestdrte Curven, in denen secundare Wellen von 
massiger Amplitude und kurzer Dauer (1-3 Stunden) auftreten, doch ist der 
tagliche Gang noch sicher erkennbar ; 

Character 4: Ziemlich gestSrte Curven, deren Gesammtbilder durch 
secundare Wellen von grSsserer Amplitude langere Zeit hindurch (6-8 
Stunden) erheblich beeintrachtigt werden ; 

Character 5: Curven mit sehr grossen, spitzen Wellen und Zacken, die 
in grosser Zahl und langerer Dauer auftreten und das normal e Bild der Cur- 
ven vollstandig entstellen. 

Bei alien Curven des Characters 3-5 wurden nun diejenigen stlindlichen 
Ablesungen, die in eine Stdrungszeit fielen, mit einem besonderen Zeichen 
versehen, gleichviel ob die Werthe zur vollen Stunde zuf^llig erhebliche 
Abweichungen von den normalen Werthen zeigten oder nicht. Eine einfache 
Auszahlnng und Zusammenstellung dieser so erhaltenen StSrungsstunden der 
Jahre 1890-95 liegt der folgenden Untersuchung zu Grunde, 



147 



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Taglicher Gang der Haufigkeit magnetischer St6rungen in Potsdam (1890—5 

1. Declination. 



























M it- 
tag 
























M* 


Manat 


X 


2 


3 


4 


5 


6 


7 


S 


9 


xo 


XX 


X 


a 


3 


4 


5 


6 


7 


8 


9 


xo 


XX 


nacW 


Jan. 


8 


9 


7 


8 


9 


5 


4 


3 


5 


4 


6 


4 


5 


5 


7 


7 


10 


15 


22 


25 


26 


24 


17 


II 


Feb. 


24 


26 


21 


18 


16 


14 


14 


9 


11 


12 


II 


10 


10 


12 


17 


19 


22 


26 


39 


40 


4i 


37 


29 


25 


Marz 


20 


23 


23 


20 


14 


10 


11 


9 


12 


13 


11 


10 


7 


7 


7 


7 


17 


3' 


37 


40 


38 


39 


33 


25 


Apr. 


14 


15 


13 


10 


10 


10 


13 


10 


6 


6 


4 


3 


2 


5 


6 


8 


9 


12 


16 


23 


24 


22 


22 


14 


Mai 


16 


18 


16 


13 


14 


15 


13 


8 


6 


5 


5 


5 


6 


7 


8 


9 


8 


7 


12 


12 


12 


16 


16 


II 


Juni 


12 


13 


10 


10 


10 


12 


15 


14 


11 


6 


2 


2 


1 


1 


1 


4 


5 


8 


5 


8 


10 


9 


11 


II 


Juli 


15 


19 


20 


17 


18 


18 


15 


11 


8 


4 


3 


2 


4 


6 


6 


7 


6 


6 


10 


10 


16 


12 


11 


7 


Aug. 


10 


14 


13 


11 


9 


II 


II 


8 


5 


3 


2 


2 


3 


3 


5 


5 


5 


4 


8 


10 


12 


12 


11 


6 


Sept 


12 


*7 


22 


21 


13 


15 


17 


14 


4 


4 


3 


3 


3 


4 


5 


7 


10 


16 


24 


23 


24 


21 


17 


12 


Oct. 


16 


19 


21 


17 


13 


II 


10 


8 


10 


11 


11 


9 


6 


8 


10 


14 


18 


23 


30 


31 


37 


39 


29 


19 


Nov. 


11 


16 


M 


14 


9 


10 


8 


7 


5 


4 


4 


6 


7 


9 


18 


26 


3i 


32 


3i 


28 


3i 


23 


22 


14 


Dec. 


9 


11 


10 


12 


10 


6 


3 


3 


3 


3 


4 


3 


5 


5 


3 


7 


13 


17 


26 


29 


29 


19 


13 


9 


Aqu. 


62 


74 


79 


68 


50 


46 


51 


41 


32 


34 


29 


25 


18 


24 


28 


36 


54 


82 


107 


117 


123 


121 


101 


73 


Win. 


52 


62 


52 


52 


44 


35 


29 


22 


24 


23 


25 


23 


27 


31 


45 


59 


76 


90 


118 


122 


127 


103 


81 


59 


Som. 


53 


64 


59 


51 


51 


56 


54 


41 


30 


18 


12 


11 


14 


17 


20 


25 


24 


25 


35 


40 


50 


49 


49 


35 


Jahr 


167 


200 


190 


171 


145 


137 


134 


104 


86 


75 


66 


59 


59 


72 


93 


120 


154 


197 


260 


279 300 273 


231 


167 





















2 


. Horizontal-In 


TEN 


sitai 


r. 


















Jan. 


14 


13 


9 


8 


10 


6 


5 


6 


7 


10 


6 


4 


3 


3 


4 


9 


11 


18 


27 


26 


30 


33 


28 


IS 


Feb. 


21 


23 


16 


16 


16 


19 


14 


12 


14 


17 


13 


12 


8 


14 


20 


16 


20 


27 


35 


37 


41 


37 


33 


25 


Marz 


24 


23 


24 


22 


15 


15 


11 


14 


18 


18 


16 


15 


'4 


20 


20 


19 


25 


36 


43 


43 


43 


45 


41 


29 


Apr. 


13 


15 


12 


14 


9 


7 


5 


5 


10 


11 


9 


7 


13 


12 


16 


21 


25 


31 


20 


24 


27 


19 


19 


M 


Mai 


16 


18 


16 


10 


9 


9 


11 


12 


16 


16 


15 


16 


18 


24 


27 


3i 


33 


32 


30 


31 


27 


24 


20 


16 


Juni 


6 


9 


10 


5 


4 


4 


7 


9 


II 


13 


11 


9 


13 


26 


35 


35 


34 


33 


23 


16 


11 


12 


11 


II 


Juli 


15 


21 


19 


14 


M 


15 


19 


15 


17 


15 


M 


18 


22 


30 


37 


38 


41 


34 


26 


23 


19 


21 


17 


IS 


Aug. 


9 


13 


13 


11 


12 


10 


11 


15 


18 


16 


14 


12 


15 


19 


20 


22 


28 


25 


18 


19 


16 


14 


13 


10 


Sept. 


21 


27 


27 


29 


21 


22 


19 


19 


16 


13 


13 


9 


16 


25 


27 


29 


37 


31 


35 


30 


31 


29 


28 


20 


Oct. 


15 


14 


17 


16 


15 


17 


17 


18 


17 


20 


15 


9 


12 


12 


16 


27 


33 


38 


34 


33 


35 


42 


35 


19 


Nov. 


13 


12 


13 


16 


16 


16 


16 


11 


9 


9 


10 


12 


11 


19 


22 


24 


26 


28 


27 


31 


3i 


24 


21 


15 


Dec. 


9 


10 


9 


10 


II 


8 


5 


5 


3 


4 


4 


2 


4 


7 


10 


14 


17 


19 


23 


25 


24 


18 


18 


18 


Aqu. 


73 


79 


80 


81 


60 


61 


52 


56 


61 


62 


53 


40 


55 


69 


79 


96 


120 


136 


132 


130 136 135 


123 


82 


Win. 


57 


58 


47 


50 


53 


49 


40 


34 


33 


40 


33 


30 


26 


43 


56 


63 


74 


92 


112 


119 


126 


112 


100 


76 


Som. 


46 


61 


58 


40 


39 


38 


48 


5i 


62 


60 


54 


55 


68 


99 


119 


126 


136 


124 


97 


89 


73 


71 


61 


50 


Jahr 


176 


198 


185 


171 


152 


148 


140 


141 


156 


162 


140 


125 


149 


211 


254 285 330 352 341 


338 335 


3i8 


284 


20S 



3. Vertical-Intensitat. 



Jan. 

Feb. 

Marz 

Apr. 

Mai 

Juni 

Juli 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Aqu. 



7 7 5 3 

12 12 10 8 

13 17 16 15 
10 13 11 9 
13 14 13 8 

3 5 5 5 

9 13 13 13 



3 6 
8 10 



7 6 

8 11 



12 12 18 14 
8998 
5 5 5 3 



2 

9 
12 

5 
8 

4 
10 

6 
12 
12 

7 
2 



1 
11 
9 
4 
6 

4 
9 
5 
7 
9 
6 



6 


7 


10 


9 


10 


9 


17 


17 


13 


10 


8 


16 


M 


16 


19 


22 


25 


21 


17 


13 


8 


13 


*5 


18 


23 


24 


22 


24 


22 


16 


6 


6 


9 


9 


10 


12 


13 


13 


10 


8 


8 


13 


13 


13 


13 


12 


14 


13 


13 


u 


3 


3 


4 


6 


5. 


3 


3 


1 


2 


2 


9 


9 


10 


10 


10 


7 


7 


5 


5 


4 


6 


8 


8 


9 


8 


7 


5 


4 


4 


I 


8 


11 


12 


8 


11 


12 


10 


12 


12 


S i 


13 


15 


U 


17 


15 


*5 


19 


22 


17 


9 


10 


13 


M 


16 


16 


17 


14 


II 


IO 


S 


3 


2 


7 


9 


10 


12 


14 


12 


II 


6 



43 52 53 49 41 29 23 14 14 13 10 9 10 17 35 45 49 52 59 63 64 71 61 3S 



Win. 32 33 29 22 20 18 14 11 13 13 10 13' 12 19 27 38 45 50 55 60 70 61 51 37 
Som. 28 38 38 32 28 24 22 23 21 17 16 14' 14 20 26 33 35 38 36 29 29 23 24 18 
Jahr 103 123 120 103 89 71 59 48 48 43 36 36; 36 56 88 116 129 140 150 152 163 155 136 93 



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DIE MAGNETISCHEN STORUNGEN IN POTSDAM 149 

Um zunachst eine Obersicht dariiber zu gewinnen, wie sich die magne- 
tischen StSrungen auf die Tageszeit vertheilen, wurde flir alle Monate fest- 
gestellt, wie haufig die einzelnen Tagesstunden in den untersuchten 6 Jahren 
gestort waren. Die gegenliberstehende Tabelle giebt diese Monats-Ubersichten 
so wie eine unmittelbar daraus folgende liber die 3 Gruppen (nach Lloyd): 
Aquinoctial- Monate, Winter- Monate, Sommer- Monate, und zwar fttr Declina- 
tion, Horizontal-Intensitat und Vertical- Intensitat. 

Nach den so gewonnenen Zahlen sind die Storungs-Curven auf Taf. I und 
II gezeichnet, die schon ein recht anschauliches Bild ttber den Verlauf 
der magnetischen Storungen geben. Sie bestatigen vollauf das, was schon 
friiher gefunden und worauf auch Herr Eschenhagen bei der Untersuchung 
der Storungen in den beiden Jahren 1890 und '91 hinwies, namlich '.'die 
characteristische Zunahme der Haufigkeit der StSrungen in den spaten Nach- 
mittag- und Abendstunden, die bedeutende Abnahme um Mittag." Auch 
scheint in der That ein secundares Maximum in den frtihen Morgenstunden, 
gegen 2 Uhr, ein secundares Minimum gegen oder bald nach Mitternacht 
einzutreten. Wahrend bei der Declination die Eintrittszeit der Maxima und 
Minima in alien Monaten fast dieselbe bleibt, wird das Haupt-Maximum 
der Storungen in der Horizontal- und Vertical-Intensitat wahrend der 
Sommer-Monate schon gegen 5 Uhr Nachmittags, also mehrere Stunden 
friiher als sonst erreicht. Sehr auffallend ist auch die betrachtlich geringere 
Haufigkeit der Storungen der Declination und Vertical-Intensitat in den 
Sommer-Monaten, in denen auch das secundare Maximum das Haupt- 
Maximum ubertrifft oder doch wenigstens erreicht. Die Horizontal-Intensitat 
zeigt dagegen umgekehrt eine grossere Anzahl von StSrungen in den Sommer- 
als in den Winter-Monaten. Ob in den letzten beiden Punkten wirklich eine 
Verschiedenheit vorhanden ist, mtissen weitere Untersuchungen ergeben. Am 
meisten gestort sind liberall die Aquinoctial- Monate, in ihnen ist auch die 
tagliche Periode der Storungen am deutlichsten ausgepragt. 

Um auch einen Oberblick Uber die Vertheilung der magnetischen 
Storungen auf die Jahreszeit zu verschaffen, ist in der nachfolgenden Tabelle 
angegeben, wie viele Stunden in den einzelnen Monaten wahrend der Jahre 
1890-95 magnetisch gestSrt waren. Hinzugeftigt sind noch die Wolf schen 
Sonnenflecken-Relativzahlen ftir denselben Zeitraum nach der Meteoro- 
logische Zeitschrift, um eine ev. Beziehung zwischen den magnetischen 
StSrungen und der beobachteten Sonnenflecken hervortreten zu lassen. 



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ISO 



G. LU DELING 



[Vol. I, No. 3] 



Jahrlicher Gang der Haufigkeit magnetischer Storungen in Potsdam (189CH 

1. Declination. 





Jan. 


Febr. 


M5rr 


April 


Mai 


Juni 


Juli 


Aug. 


Sept. 


October Novbr. 


Decbr. 


Aqui- 
noctien 


! 

Winter Sommrr 


1890. . . 


12 


26 


4 


% 


5 


6 


12 


4 


10 


35 


22 




49 


60 


27 


1891. . 


10 


51 


51 


49 


54 




17 


20 


77 


68 


59 


59 


245 


179 


91 


1892... 


68 


140 


185 


88 


70 


46 


94 


39 


44 


104 


50 


44 


421 


302 


249 


1893... 


55 


68 


62 


17 


7 


50 


31 


49 


69 


72 


59 


41 


220 


223 


137 


1894... 


69 


140 


90 


66 


73 


50 


66 


56 


76 


71 


105 


46 


303 


360 


245 


1895.. 


34 


76 


75 


57 


49 


39 


32 


15 


34 


70 


85 


62 


236 


257 


135 


Summe 


248 


501 


467 


277 


258 


191 


252 


183 


310 


420 


380 


252 


1474 


I38l 


884 3 


Procent 


6.6 


13.4 


12.5 


7.4 


6.9 


5-1 


6.7 


4.9 


8.3 


1 1.2 


10.2 


6.8 


39-5 


37-0 


23-5 















2. 


Horizontal-Intensitat. 














1890... 


12 


35 


32 


13 


36 


32 


58 


40 


43 


67 


44 


6 


155 


97 


166 




1891... 


26 


57 


99 


79 


121 


23 


54 


49 


199 


105 


65 


61 


482 


209 


247 




1892... 


67 


119 


181 


75 


105 


66 


160 


9i 


66 


58 


60 


28 


380 


274 


422 


J 


1893.. 


45 


5i 


50 


22 


26 


93 


33 


68 


67 


68 


46 


45 


207 


187 


220 




1894.. 


80 


135 


108 


74 


79 


83 


140 


80 


136 


88 


97 


56 


406 


368 


3«2 


1 

- 

i 


1895... 


78 


109 


123 


95 


no 


61 


72 


45 


63 


140 


120 


81 


421 


388 


288 


Procent 


308 


506 


593 


358 


477 


358 


517 


373 


574 


526 


432 


277 


2051 


1523 


1725 


Summe 


5.8 


9.6 


1 1.2 


6.8 


9.0 


6.8 


9.8 


7.0 


10.8 


99 


8.1 


52 


38.7 


28.7 


32.6 


















3. Vertical- 


Intensitat. 














1890. .. 


16 


# % 


11 




15 


8 


15 


6 


15 


73 


15 


.. 


99 


3i 


44 




1891... 


3 


18 


17 


31 


58 


7 


15 


12 


24 


27 


9 


13 


99 


43 


92 




1892... 


62 


98 


148 


79 


103 


44 


99 


37 


41 


67 


31 


23 


335 


214 


283 




1893.. 


37 


33 


34 


7 


8 


8 


13 


34 


19 


18 


33 


9 


78 


112 


63 




1894.. 


43 


103 


69 


23 


15 


25 


19 


12 


37 


20 


37 


16 


149 


199 


71 




1895... 


4 


28 


21 


28 


28 


5 


24 


16 


34 


71 


68 


54 


154 


154 


73 


a 


Summe 


165 


280 


300 


168 


227 


97 


185 


117 


170 


276 


193 


115 


914 


753 


626 


Procent 


7.2 


12.2 


131 


7.4 


9.9 


4.2 


8.1 


5-1 


7.4 


12.0 


8.4 


5.0 


39.9 


32.8 


273 














Wolf's 


Sonnenflecken-Relativzahlen 


• 










1890.. . 


5.3 


0.6 


5-1 


1.6 


4.8 


1.3 


1 1.6 


8.5 


17.2 


1 1.2 


9.6 


7.8 


35-1 


23.3 


26.2 




1891... 


17.1 


23.0 


1 0.0 


19.4 


43-2 


48.7 


59.1 


32.6 


52.1 


50.4 


41.0 


30.6 


'31-9 


111.7 


183.6 


i 


1892... 


72.4 


72.4 


52.5 


69.6 


79.2 


76.6 


77.9 


102.6 


62.2 


74.8 


67.1 


77.8 


259.1 


289.7 


336.3 


1 


1893.- 


78.3 


72.4 


65.7 


88.1 


82.9 


88.2 


90.6 


129.2 


77.5 


80.0 


75.1 


938 


3II-3 


319.6 


390.9 


i" 


1894- •• 


83.2 


84.6 


52.3 


81.6 


101.2 


98.9 


106.0 


70.3 


65.9 


75.5 


56.6 


60.0 


275.3 


284.4 


376.4 


1 ! 


1895.. 


63.2 


67.5 


62.1 


76.8 


67.3 


71.3 


48.1 


69.0 


58.5 


66.1 


42.8 


74.4 


263.5 


247.9 


255.7 


1 


Summe 


319.5320.5 


2477 


337.1 


378.6 


385.0 


393.3 


412.2 


333.4 


358.0 


292.2 


344-4 


1276.2 


1276.6 


1 569.1 


J4l 


Procent 


7-7 


7.8 


6.0 


8.2 


9.2 


93 


9.5 


1 0.0 


8.1 


8.7 


71 


8.4 


31.0 


31.0 


38.0 


1 



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DIE MAGNETISCHEN ST&RUNGEN IN POTSDAM 1 5 1 

Auf Taf. Ill ist das mittlere Auftreten der StSrungen sowie der Sonnen- 
flecken in den einzelnen Monaten in Curven dargestellt (nach Procenten der 
Haufigkeit). Irgend welcher parallele Gang der beiden Erscheinungen 
zeigt sich darin nicht. Auch ein Vergleich der Jahres-Summen bringt 
zunachst noch keinen auffalligen Zusammenhang. Allerdings dlirfte der 
Zeitraum von 6 Jahren ein zu kurzer sein, als dass man aus dem hierbei 
gewonnenen Materiale irgend welche Schllisse auf einen etwa vorhandenen 
parallelen Gang der magnetischen StSrungen mit den Sonnenflecken und 
deren elfjahriger Periode ziehen kSnnte. Wir behalten uns jedoch vor, nach 
Ablauf der elfjahrigen Periode auf diese Frage zuriickzukommen. Wie 
oben schon angedeutet, ist jedoch das doppelte Maximum der magnetischen 
Storungen zur Zeit der Aquinoctien und das Minimum in den Sommer- 
Monaten und im December ausserordentlich hervortretend. Diese Thatsache 
wurde bereits von A. von Humboldt gefunden und spater besonders von 
Sabine an einem sehr umfangreichen Beobachtungs- Material bestatigt. Ob die 
beiden Monate Mai und Juli thatsachlich derart herausfallen, dass sie einc 
grossere Anzahl StSrungen zeigen, als die benachbarten Monate, muss eine 
systematische Untersuchung einer langeren Beobachtungsreihe ergeben. 
Sollte es der Fall sein, so wlirde man hier vielleicht einen merkwlirdigen 
Farallelismus zu dem doppelten Ge witter- Maximum haben, das zuerst Herr 
von Bezold fur die Monate Mai und Juli nachwies (Pogg. Ann, 1 36, 1 869, 
pag. 513), und auf welcher auch Herr Leonhard Weber bei seinen Tageslicht- 
Messungen in Kiel geflihrt wurde (Schriften des Natutw. Vereins fiir 
Schleswig-Hohtein, Bd. X, Erstes Heft). 

Eine fast vollige Obereinstimmung findet sich nun aber in Her Periode 
der magnetischen Stoning und der des Polarlichts, und zwar sowohl in der 
taglichen wie in der jahrlichen (s. Taf. II und III. Die Nordlicht-Curven 
gelten fiir Oxford resp. das mittlere Europa zwischen 46 und 55 ° N.Br.). 
Ob dies fiir alle Breiten der Fall ist, oder wie sich die Beziehungen mit der 
Entfernung von den Polen andern, mtissen weitere Untersuchungen, beson- 
ders auch von nahe dem Aquator gelegenen Stationen zeigen. Die Aufgabe 
der vorliegenden Arbeit war im Wesentlichen nur, die von Herrn Eschen- 
hagen als vorlaufiger " Versuch '* vorgeschlagene Classification der magne- 
tischen Curven in Bezug auf die StSrungen (Character 3-5) zu erproben. Dass 
diese Probe die grosse Nlitzlichkeit der libera us einfachen Methode ergeben 
hat, darf wohl mit Recht aus den gewonnenen Resultaten geschlossen wer- 
den. Meines Erachtens ware es daher hSchst wunschenswerth, wenn auch 
an anderen Observatorien dasselbe Verfahren angewandt wlirde. 



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LETTER TO EDITOR 



OLD MAGNETIC DECLINATIONS: THE WORK ENTITLED 
"AIMENEYPETIKH," etc. 1 

Das von Herrn Schott auf S. 87 dieser Zeitschrift erwahnte Werk 
aus dem Jahre 1599, das Beobachtungen der magnetischen Declination 
enhalt, ist nur ein Abdruck der kleinen Schrift des beriihmten hollan- 
dischen Mathematikers Simon Stevin, die von seinem Landsmann 
Grotius ins Lateinische ubersetzt wurde und 1599 zu Leiden unter 
dem Titel " Aifuvtvpeructf sive Portuum investigandorum ratio" erschien. 
Anscheinend gleichzeitig erschienen auch Ausgaben in hollandischer, 
franzosischer und englischer Sprache. Die letztere ("The Haven- 
Finding Art") besorgte der bekannte Edward Wright. 

Stevin benutzte zum Theil die Angaben von P. Plancius, einem 
calvinistischen Prediger in Amsterdam, dessen Verdienste um die 
Kartographie und den Erdmagnetismus noch nicht geniigend klar- 
gestellt sind. Plancius scheint eine Erdkarte oder einen Erdglobus 
entworfen zu haben, auf dem er alle damals bekannt gewordenen 
Werthe der magnetischen Declination eintrug. Veroffentlicht wurde 
diese Karte meines Wissens nicht. Es ware sehr erwiinscht, wenn ein 
hollandischer Gelehrter, dem allein das gedruckte wie ungedruckte 
Material zu Gebote stehen diirfte, dieser Frage einmal seine Aufmerk- 
samkeit schenken wiirde. 2 G. Hellmann. 

Berlin, den 26. April 1896. 

1 Sec p. 87 of this Journal. In the title there given the word Portunus should 
have been Portuum, — Ed. s 

2 Through the courtesy of Dr. Artemas Martin of Washington City, the Editor had 
the opportunity of looking over a copy of this work. Many of the magnetic declina- 
tions given will also be found in Kircher's Ars Magnesia, Herbipoli, 1 63 1, pp. 45 and 
46. It is a matter of interest that Grotius uses the word declinatio when referring to 
the magnetic declination, whereas, as will be recalled, Gilbert in his De Magnete, 
published a year later, used the same word to mean the magnetic inclination, and the 
word variatio to mean declination. Gilbert's declinatorium — an instrument to 
measure the inclination — is now referred to as inclinatorium. Kircher in his works 
uses declinatio and inclinatio according to the modern accepted meanings. As 
Gilbert's great work was considered such a standard one, it is a matter of some sur- 
prise that his adopted nomenclature did not prevail. — Ed. 

153 



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NOTES 



The honorary degree of Doctor of Laws was conferred at Lord Kelvin's 
Jubilee upon two of the Associates of the Journal, Professors Abbe and 
Mascart. 

" So far the Journal seems a great success." — A, Schuster, Manchester. 
" Mit grosser Freude habe ich das Erscheinen des ersten Heftes des Journals 
gegrlisst ; und ich habe dasselbe von meiner ganzen Satisfaction gefunden." 
— L. Palazzo (Rome). 

In commemoration of Professor Neumayer's seventieth birthday, which 
took place on June 21, the German Meteorological Society decided to pre- 
sent him with an album of the photographs of the members as a token of 
their high esteem. The Journal extends to the genial director of the Ger- 
man Naval Observatory its heartiest congratulations and trusts that the sci- 
ence for the advancement of which he has worked so zealously in the past 
may long be enriched by his labors. 

• We regret to be obliged to record the death of Mr. Charles Chambers, F. 

' R. S. f for thirty years director of the Colaba Meteorological and Magnetic 
Observatory at Bombay. According to Nature s extract from the Times, 
Mr. Chambers was born at Leeds, Yorkshire, on May 30, 1834, being thus 
62 years of age at the time of his demise. After finishing his education in 
his native place, he secured an appointment in the Kew Observatory (Balfour 
Stewart then Superintendent) which he left in October 1 863 to take up the 
post as assistant to the Director and Chief Superintendent and Electrician of 
the Indo-European Telegraph Department, Persian Gulf Section. In Octo- 
ber 1 865 he was temporarily appointed Superintendent of the Government 
Observatory, Bombay. After acting in that capacity for over two years he 
was confirmed in the appointment in January 1 868, and continued to hold 
that office till November 1 886, when he was given the appointment of Director 
of the Colaba Observatory, which office he was holding at the time of his 
death. He was elected a Fellow of the Royal Society in 1 869. He was 
also appointed a Fellow of the Bombay University in 1872, and a member of 
the syndicate of the same university from 1879 *° 1890. 

A list of his published papers will be given in a future number of the 
Journal. 

Professor N. A. Afoos, of the Elphinstone College, Bombay, has been 
elected to succeed the late Mr. Chambers as Superintendent of the Colaba 
Observatory. 

Simultaneous Observations of the Magnetic Perturbations. Professor 
Eschenhagen informs us that in response to the circular sent out , various 
magnetic observatories, among which are Batavia, Washington, and possibly 
Melbourne, have cooperated with the Potsdam Magnetic Observatory in 
making these observations at the times fixed upon (cf p. 61). At the date of 

154 



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NOTES 155 

writing (May 1 ) he had received results from twelve stations. During the 
time of observation on February 28 a disturbance of " no inconsiderable M 
magnitude was in progress. The discussion will consequently prove of 
great interest. Those who have read his most interesting contribution in 
the last number of the Journal cannot have failed to recognize the impor- 
tance of the work he has undertaken. It has been known for some time 
that the large magnetic disturbances — the so-called magnetic storms — are, 
as far as can at present be determined, practically simultaneous in their 
occurrence over large areas of the Earth's surface, if not, indeed, over the 
entire Earth. Violent perturbations take place, however, at comparatively 
rare intervals. On the other hand, smaller fluctuations reveal themselves to 
greater or less extent at all times. The question is, do some of these minor 
perturbations, like the larger ones, make themselves felt over wide areas at 
about the same absolute time ? If so, then their origin, like that of major 
ones, would seemingly have to be cosmical. Or are they of a purely local 
character, as, for example, such fluctuations due to thunderstorms as have 
been observed at some observatories ? Do they, like the diurnal variation, 
respond to local time and not to absolute ? As will be recalled, the result 
of the preliminary observations carried on in conjunction with the Wilhelms- 
haven Observatory, 36o km distant, as summed up by Eschenhagen in the 
paper referred to was: "that among the many crests which the diurnal 
curves of magnetic force at both stations revealed, not one was to be referred 
to a purely local cause, but that the large disturbances as well as the very 
small ones, amounting in intensity to but 0.00003 C. G. S., probably occur 
simultaneously, over a large area.*' The results of the latest observations, 
covering the larger portion of the globe, will therefore be looked forward 
to with great interest. Aside from the intrinsic value of such work as this, 
the international character of it, inviting the harmonious cooperation of all, 
cannot fail to prove of the greatest value to the cause and to the workers. It 
will be seen elsewhere that the special work before us is down for discussion 
at the International Meteorological Conference. 

The Action of Electric Currents on Mine Surveying Instruments. From 
Electricity we quote the following: 

"Mr. W. Lenz contributes to the April 18 issue of the Engineering and 
Mining Journal an article on the above subject as a result of some tests 
made at a point underground at a horizontal distance of about 150 yards [137 
meters] from the rails of an electric railway and 1420 feet [433 m.J below it. 
Two series of tests were made with a Fennel's magnetometer, one in the 
daytime while the road was in operation and one at night when it was not. 
The former showed great variations within slight intervals of time, and the 
latter a very regular curve. He also found considerable effect from the 
safety lamps while hot, even though they contained no magnetic material. 
This he ascribes to the thermo-electric currents which were absent, as well as 
their effects when the lamps are cold. He concludes that the mine surveyor, 
before making magnetic observations with delicate instruments, should 
carefully test his lamp." 



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156 MOTES [Vol. I. No. 3] 

Deutsche Orthographie. Urn eine mSglichst einheitliche Schreibweise 
des Deutschen in unsere Spalten einzufuhren, hat die Redaction an die 
Herren Mitarbeiter in Deutschland und Osterreich ein Rundschreiben ergehen 
lassen und denselben einige diesbeziigliche Fragen vorgelegt. Fast samt- 
liche Antworten sind bereits eingegangen. Die Herren haben sich mit 
dankenswerter Bereitwilligkeit allem angeschlossen, was Nicht- Deutschen zur 
Erleichterung dienen kann und haben teilweise sogar weitere Vorschlage in 
demselben Sinne gemacht. In dem Dilemma zwischen alter und neuer 
Orthographie haben sich die meisten Herren nicht fiir eine consequente 
Durchfiihrung der letzteren, sondcrn nur flir teilweise Verbesserung ent- 
schieden. Jedenfalls entspricht es dem Wunsche Aller, wenn wir 

1. Fremdworter mSglichst mit ihrer Ableitung in Einklang bringen 
(Curve, nicht Kurve, etc.). 

2. Zwar die alte Orthographie zu Grunde legen, aber eingeflihrte Ver- 
besserungen, soweit sie eine wirkliche Erleichterung gewahren, beriick- 
sichtigen. Hierbei wird allerdings bei einigen Wortern der Willkiir ein 
geringer — wohl ganz unbedenklicher — Spielraum gelassen. 

3. Unbequeme, lange Composita durch Bindestrich trennen: "Maximal- 
Abweichung. M (Vorschlag des H. Eschenhagen.) 

Auf diese Weise glauben wir der liberal 1 hervortretenden Tendenz, der 
internationalen Brauchbarkeit unserer Zeitschrift Vorschub zu leisten, am 
besten gerecht zu werden. 

Einige weitere, der Vollstandigkeit halber aufgef Unite Punkte (z. B. 
Kleinschreibung der Hauptwdrter) sind unserer Erwartung gemass abgelehnt 
worden. 

Schliesslich wollen wir noch bemerken, dass jeder der Herren Mitarbeiter, 
dem besonders daran liegt, dass seine Rechtschreibung ungeandert bleibe, 
sich dieses Vorrecht durch eine dahingehende Bemerkung sichern kann. 

P. W. 

The International Meteorological Conference to be held in Paris in 
September i8q6. Through the courtesy of the Secretary of the Committee 
Mr. Robert H. Scott, we are enabled to reprint from the preliminary pro- 
gramme the questions of special interest to magneticians which are proposed 
for discussion. It is a source of great gratification to see terrestrial mag- 
netism so well represented. The conference might well be called the 
meteorological and magnetic conference. 

3. Professor W. L. Moore, Washington. The solar magnetic period 26.67928 
days as the natural mode of classifying solar, physical, and terrestrial meteorological 
phenomena. The desirability of its introduction for general use in the year 190 1. 

27. Professor E. Mascart, Paris. Atmospheric electricity. 

28. Idem. Terrestrial magnetism. 

29. Professor von Bezold, Berlin, and Professor Eschenhagen, Potsdam. 
General principles should be introduced for the publication of magnetic observa- 
tions:— a. The values obtained should be given for the different observing hours in 
absolute measure, freed from the variations of the zero of the scale (base value) and 
of temperature, b. It should be stated accurately in what way the scale readings 
have been converted to absolute measure, and to what extent the temperature has 



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NOTES 157 

been taken into consideration, c. It is desirable that for each day the values should 
be given for each complete hour. d. The same notation should be generally 
employed: — H for horizontal force, X for the northern component, Y for the western 
component, Z for the vertical force, and V for the potential, e. In calculating 
monthly means all days are to be taktn into consideration. It is left open to each 
director to give, in addition, means calculated without taking disturbed days into 
account. /. It is very desirable that for the monthly means there should be calcu- 
lated and published at least the values of the components X, Y, Z, and also for the 
monthly means of the separate observation hours, the differences of the components 
A X, A Y, A Z from the mean of the month. 

30. Idem. General principles should be laid down for magnetic surveys: — a. The 
density of the system (*.*., the closeness of the stations inter se). b. The elimination 
of variations by means of the observations at the base stations, c. The reduction of 
the observations to a definite epoch, d. The comparison of the instruments employed 
in the different surveys. 

31. Idem. It is desirable that all institutes which publish magnetic charts should 
give additional tables containing the magnetic elements, and, if possible, also the 
components for convenient points of intersection of the geographical coordinates. It 
is equally to be desired that the data on which these charts have been constructed 
should be published in the fullest manner possible. 

32. Idem. The distribution of magnetic observatories over the globe should be 
discussed. 

33. Idem. Arrangements should be made for taking international simultaneous 
observations. 

34. M. S. Lemstrom, Helsingfors. The investigation of earth currents. 

35. Rev. Father Faura, S. J., Manilla. It is desirable that the International 
Conference should give practical instructions as to how earth currents are to be 
observed in order to find out their intensity and direction, and their relation to other 
meteorological phenomena. 

Old Observations of Magnetic Declination at Vienna. In the Meteorology 
ische Zeitschrift (January 1895, P- 3^), Professor Hellmann calls attention to 
some old declinations observed at Vienna, which have not been noticed else- 
where. He found them in a rare old book containing chiefly early meteoro- 
logical observations made at Vienna, by J. J. W. von Peima. (J. J. W. stands 
for Johannes Ignatius Worb.) The author of the book found " in suburbano 
Landstrazzie " (of Vienna) the declination : 

n° 52^' W. on July 25, 1715. 
n° 58' W. on July 22, 1716. 

Hellmann shows furthermore by citing the following extract: "Ex vetus- 
tis codicibus habemus quod Arctodromicum abhinc 60, 70 Annis, hie Viennae 
O declinaverit " that the agonic must have passed through Vienna in about 
the year 1 640, which agrees well with the observation given by Hansteen in 
his Mag. der Erde, App. p. 10, viz., zero for 1638, no reference to source 
being given. Hellmann thinks that this value is due to the Jesuit father Cobau. 
A. Kircher, in his Magnes, etc., Roma, 1641, p. 455, or 1644, p. 329, gives the 
following for Vienna : 

P. Andreas Cobauius S. J., o° o', declination, 48 ° 20' latitude, but no date. 

The only other early observation given by Hansteen is that by Chappe and 
Liesganig, December 1760, value 13 o'w. 

Attention is also called to the word that von Peima used for compass, viz., 
"Arctodromicus." 



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158 



NOTES 



[Vol. I. No. 3J 



Der nor male Erdmagiutismus. Under this title Professor W. von Bezold 
presented to the Berlin Academy of Sciences, on December 5, 1895, a con- 
tinuation of his researches with respect to the normal or mean distribution 
of the Earth's magnetism. He sums up his conclusions as follows: 

" Die auf Grundlage des besten gegenwartig zuganglichen Materials aus- 
gefuhrten Untersuchungen berechtigen vollauf dazu, von einem normal en 
Erdmagnetismus zu sprechen, da zwischen den aus der einfachen Fonnel 
berechneten Werthen und den aus der Gauss'schen Reihe sowie unmittelbar 
aus Beobachtungen abgeleiteten Werthen fur das Potential sowie fiir die 
Componenten eine weitgehende Obereinstimmung besteht. 

Das Potential dieser normalen Vertheilung wird durch den von der geo- 
graphischen Lange unabhangigen Theil des ersten Gliedes der Gauss'schen 
Reihe dargestellt. Die Formeln lauten dementsprechend : 



^ = ^' o sin0, 



X v =g to cosp t 



Z ¥ = 2£ l '° sin p. 



Diese Formeln sind die gleichen, wie man sie erhalten wiirde, wenn die 
Erde eine durch und durch parallel zur Erdaxe gleichmassig magneti$irte 
Kugel ware, oder wenn sie von einem dieser Vertheilung gleichwerthigen 
Systeme von Stromen umflossen ware. 

Es scheint kaum nothig darauf hinzuweisen, dass sich diese Formeln auch 

ausserordentlich leicht geometrisch 
versinnlichen lassen. Troudem 
balte ich es fur gut, eine hierauf 
beziigliche Figur mitzutheilen. 

Bedeutet der um C geschla- 
gene Kreis den Umfang der in 
orthographischer Projection dar- 
gestellten Erde, NS deren Axe, 
so erscheinen die nach gleichen 
Differenzen von V weiter schrei- 
tenden Gleichgewichtslinien als 
lauter gleich weit von einander 
abstehende, dem Aequator paral- 
lele Linien. 

Halbirt man alsdann den nach 
dem Schnittpunkte D einer solchen 
Geraden mit der Peripherie gezo- 
genen Halbmesser, und errichtet man in dem Halbiringspunkte E eine Senk- 
rechte EG von solcher Lange, dass EG = 2EF ist, so besteht, wie leicht zu 
Ubersehen, fur den Winkel GDE = { die Beziehung tgt = 2/^/3, d. h. i* ist 
der normale Inclinationswinkel in dem Punkte D. Die Uber D hinaus ver- 
langerte Gerade DG aber ist die Tangente, welche man in D an die Gleich- 
gewichtsflache legen kann, und bezeichnen die kurzen Geraden, welche man 
an den Schnittpunkten der Gleichgewichtslinien mit der Peripherie findet, 
Stlicke der entsprechenden Tangenten. 

Man gelangt demnach auf dem Wege der Mittelbildung aus den einzelnen 
Componenten sowie fiir das Potential nach ganzen Parallelkreisen zu einer 
ausserordentlich einfachen und ubersichtlichen Vertheilung der erdmagne- 
tischen Krafte, die man deshalb wohl als die normale bezeichnen darf. 

Den in einem gegebenen Augenblicke bestehenden magnetischen Zustand 
der Erde aber wird man zweckmassig als Obereinanderlagerung eines oder 
mehrerer storenden Systeme Uber dieses normale System betrachten. 

t)ber eine Anwendung dieses Gedankens auf die tagliche Variation der 
erdmagnetischen Kraft hoffe ich in nicht zu ferner Zeit Mittheilung machen 
zu kbnnen." 




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REVIEWS 1 59 

REVIEWS. 
ON THE NATURE AND THE ORIGIN OF THE AURORA BOREALIS. 

Paulsen, A.: " Effet de rhumidite" de fair et action du champ magnitique 
terrestre sur PasPect de Paurore boriale" Bulletin de l'Acad^mie Roy. 
des Sci. et des Lett, de Danemark, Copenhague, pour l'annSe 1895. 
Partly translated in the Meteor. Zeit., Jan. 1896. 

. " Sur la nature et rorigine de Vaurore bore" ale'' Ibid, % 1894. 

In these two contributions Adam Paulsen emphasizes the meteorological 
side of the question, "What is an Aurora ?" as distinguished from the many 
ingenious physical theories which have been put forward. Both of the papers 
are valuable additions to our knowledge of auroral formation and have a 
charm in this that no stretching of the observed conditions is necessary in 
order to accommodate them to the views held by the writer. Our author first 
gives some experimental observations which show, he thinks, the existence 
and direction of electrical currents in the air and the influence of the aurora 
upon the electrical potential of the air near the ground. As yet there has 
been no general law discovered covering the relations of the magnetic needle 
and auroral displays. Great auroral displays are for the most part accom- 
panied with marked perturbations of the needle ; but the observations of the 
circumpolar parties of 1882-3 demonstrated beyond a doubt that there are 
many auroral displays, particularly of the quiescent type, which are not accom- 
panied with disturbed needle readings. It is plain that for sometime we 
have been classifying under one term — aurora — phenomena which are some- 
what alike in appearance, but yet are of different origin. Many of the diffi- 
culties now met in reconciling sun-spot, auroral and magnetic periodicities 
will disappear when it is understood that there is one set of phenomena widely 
extended and magnificent in color which are accompanied with magnetic dis- 
turbances and more or less solar commotion ; and another class of auroral 
displays which are local in character and more in the nature of manifestations 
of atmospheric electricity. With these preliminary remarks we proceed to 
abstract from the two papers. 

" The great displays which cover a large portion of the sky must have a 
peculiar effect upon the needle since the position and intensity of the light are 
constantly changing. Moreover there is the disturbing effect of the earth 
currents which in general a strong aurora induces. But there is one auroral 
appearance which I have only seen during my stay in Greenland which is 
noteworthy. It resembles a curtain hung vertically and has a very rapid motion. 
At Godthaab, on the west coast of Greenland, such a display comes up rapidly 
from the magnetic south, passes the zenith and then stretches away to the 
north. Its great velocity makes one think that its elevation above the ground 
must be small. If such an aurora is due to a charged mass there should be 
a change in sign in the deflection of the magnetic needle, the moment the 
aurora passes the zenith. At Godthaab I twice saw such displays, but unfor- 
tunately was too far away from the magnetic needle to tell whether it was 
affected or not. But M. Vedel, whom 1 had asked to study such matters 
while on the staff of Ryder in the expedition to Scoresby Sound in 189 1-2, 
has repeatedly seen small auroral draperies move with great rapidity from the 
south to the north, and every time the needle has been observed to move 
toward the west with the approach of the aurora. When the aurora passes 
the zenith the needle oscillates and returns to the position which it held before 
the aurora appeared, or deviates to the east when the aurora stretches away 



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I 60 RE VIE li 'S [Vol. 1 . No. 3J 

to the north. These observations show that these auroral curtains are due to 
electrical currents moving from the bottom upward. The electrical potential 
then decreases toward the top in these auroral curtains, and we think that our 
experiments confirm those of Vedel in proving that the potential of the air 
near the surface of the earth decreases and may even become negative dur- 
ing an auroral display." 

Our author then refers to observations made with an insulated metallic 
point elevated in the air, the supporting pole erected on the top of a hill about 
ninety meters above sea level. By means of a delicate Thomson reflecting 
galvanometer, astatic, they were able to follow changes in the potential. It 
was difficult, of course, to preserve a proper insulation and likewise the swing- 
ing of the wire caused by the wind. The current was considered negative 
whenever the potential of the ground slightly exceeded that of the air. At 8 
o'clock, November 12, the spot of light upon the galvanometer scale slowly 
approached the zero point, indicating a negative current. At the same moment 
there appeared an aurora. At 8:30, when the aurora was brightest, the gal- 
vanometer indicated no current. And so on through the night, changes in the 
aurora were accompanied with movements of the needle. Our author believes 
that the effect of an aurora upon the magnetic needle is also shown by the 
ordinary diurnal curve of declination at Godthaab. We have not space to give 
Paulsen's statements as to the various forms of auroral curtains, beams and 
draperies and the relationship which be traces between their position and the 
deviations of the magnetic needle. He comes to the conclusion that the 
aurora must be considered as a. fluorescence Produced by the absorption of radi- 
ant energy originating in the upper regions of the air. Physically speaking, 
it is not the aurora which emits the luminous rays, but the invisible rays which, 
undergoing transformation appear as an auroral drapery or curtain. The 
explanation of the aurora generally given, namely that it is a discharge of 
electricity in ra rifled air, has some difficulties, for it is known that in arctic 
regions displays have been seen at the very bottom of the atmosphere and 
under ordinary pressure condition. How could we explain the enormous dif- 
ference of potential which would be necessary, and how could a current strong 
enough to make the air incandescent at a pressure of about one atmosphere 
stop suddenly without continuing on to the ground ? If the auroral rays are 
electrical currents the paths would be determined by the conductivity of the 
air ; but the auroral rays have always a rectilinear position and when dis- 
placed, which is with enormous rapidity, come back to the initial position. 
Finally, observations show that great auroral displays may occur without sen- 
sibly disturbing the needle. We can suppose that the electric currents are 
purely secondary effects of the aurora. It is not an electrical current which 
causes the aurora, but the aurora which causes electrical currents. Paulsen 
then traces at some length the resemblance of the auroral light to radiations 
emitted by the negative pole of a tube in which the air has been, rarified and 
in fact considers the auroral light as somewhat analogous to the cathode 
radiation. As to the source or better seat of origin of the auroral energy 
Paulsen assumes the existence of a layer of negative electricity residing in the 
upper regions of the atmosphere. 

It should be noted in connection with Paulsen's views that Bigelow in the 
American Journal of Science, August 1895, says with reference to the trans- 
formation of ether vibrations in the atmosphere: " Like phosphorescence and 
uorescence we may regard the auroral light as the product of the transforma- 
on of vibrating energy into the required period by means of the atomic and 
lolecular elements of the air, as a system of step-up transformers." 

Alexander McAdie. 



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REVIEWS l6l 

DETERMINATION OF THE MAGNETIC ELEMENTS IN SWEDEN. 

Carlheim-GyllenskOld, V.: Determinations des iliments magnittques 

effectue'es sur la glace de quelques lacs en Suede pendant fhiver 1889. 

Bihang till K. Svenska Vet.-Akad. Handlingar. Bd. 20, Afd. 1, No. 8. 

Stockholm, 1895. 32 S. 8°. 
. Magnetiska deklinations-observationer utfbrda pd svenska kuster af 

svenska s/'oofficerare dren /8j2-/8jj. Ofversigt af K. Vet.-Akad. 

FSrhandlingar, 1894. No. 2. Stockholm, 1894. 10 S. 8°. 

Observations magniHques faites Par Th. Arwidsson sur les cdtes de la 



Suede pendant les annies 1 860-1. K. Svenska Vet.-Akad. Handlingar. 
Bd. 27, No. 8. Stockholm, 1895. 22 S. 4 . 

Der Zweck des ersten der obigen Aufs&tze war, zu untersuchen, ob die 
haufigen Abweichungen localen Charakters, diebei einer frtiheren (1886) vom 
Verfasser unternommenen magnetischen Aufnahme slidlichen Schwedens 
am Lande aufgefunden worden, durch sehr nahe gelegenen eisenhaltigen 
Bergarten zu erklaren waren. Die Bestimmungen der drei Elemente wurden 
mit einem Lamont'schen Reise-Theodolit ausgefiihrt. Die Nad el lasst sich 
bekanntlich nicht umlegen, sodass der Collimations-Fehler eigens bestimmt 
werden musste ; schwieriger aber, und daher ungenauer, ist die Bestimmung 
der nicht aufzuhebenden Torsion durch Ablenkungs- Beobachtungen. Win- 
diges Wetter verhinderte Schwingungs-Beobachtungen wahrend der Reise, 
so dass die Horizontal- 1 ntensitat nur durch Ablenkungen gemessen wurde ; 
dabei wurde die Anderung des magnetischen Moments der Zeit proportional 
angenommen. Die Inclination wurde durch Induction der Vertical- 1 ntensitat 
in weichen Eisenstaben bestimmt, eine Methode, die jedoch keine grossere 
Genauigkeit zulasst. Der Vergleich mit den durch Interpolation, unter 
Berucksichtigung aller Beobachtungen der frtiheren Aufnahme, ermittelten 
Werten ergab, dass die Declination auf den Binnenseen durchweg kleiner, 
und zwar im Mittel um 5 1 ' , beobachtet wird, die Horizontal- 1 ntensitat durch- 
weg grSsser, im Mittel um 12 Einheiten der vierten Decimale ("C. G. S.), die 
Inclination meistens grosser (Mittel aus alien Vergleichungen 6'); doch fan- 
den sich auch kleinere negative Abweichungen. Die einzelnen Differenzen 
weichen aber bei alien drei Elementen betrachtlich von einander ab, woraus 
zu schliessen ist t dass man auch durch Beobachtung auf dent Eise grosserer 
Seen nicht von rein localen Perturbationen befreit werden kann. 

Im zweiten Aufsatz hat Verf. Beobachtungs-Reihen der Declination an 
der schwedischen Kliste und am WenerSee, ausgefiihrt von V. af Klint (1852 
und 1853) und Th. Arwidsson (1854 und 1855) einer neuen Berechnung 
unterzogen. Dieselben sind zwar publicirt, aber m$t grosseren constanten 
Fehlern behaftet. Klint beobachtete mit zwei Azimuthal-Compassen, von 
denen die eine, mit B bezeichnet, jetzt einen Index-Fehler von — 63 '.1 zeigt, 
die andere einen solchen von — 24 ' .6. No. B hatte aber vom Beginn an einen 
anderen und kleineren Index- Fehler, welcher, so gut es anging, durch Ver- 
gleich mit spateren Beobachtungen an denselben Pl&tzen, reducirt zu der- 
selben Epoche, bestimmt wurde; der jetzige grSssere Index-Fehler wurde 
durch Unmagnetisirung der Nadel wahrend der Reise herbeigefUhrt. Die 
Bestimmungen Arwidsson's waren mit einem Lamont'schen Theodolit mit 
umlegbarer Nadel ausgefiihrt ; dabei scheint aber die Torsion des Aufhange- 
fadens nicht aufgehoben gewesen zu sein ; aus spateren Beobachtungen fol- 
gert Verf. eine Torsion von der Reihe nach 108 '.7 (10 Comparationen) ; 103 '.6 
(7Comp.); 108 '.2 (3 Comp.); eine sehr befriedigende Obereinstimmung, 



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162 REVIEWS [Vol. I. No. 3l 

wenn man bedenkt, dass eine so grosse Torsion sich auch mit der Zeit ver- 
andert. 

Der dritte Aufsatz enthalt die vom Verfasser berechneten Beobacbtungen 
Arwidsson's i860 und 1861 der Horizontal- 1 ntensi tat und Inclination mit 
einem Lamont'schen Tbeodolit ; auch werden die frtiher publicirten gleich- 
zeitigen Bestimmungen der Declination beigegeben, reducirt wegen taglicher 
Variation. Die Horizontal- Intensitat wurde meistens nur durch Ablenkungen 
bestimmt ; um dabei die Anderung des magnetischen Moments mit der Zeit 
beachten zu kSnnen, geht Verfasser von anderweitig bekannter Horizontal- 
Intensitat in Stockholm, Copenhagen und Christiania aus. Die Haupt- 
Constanten waren von Lamont bestimmt. Die Inclination wurde durch 
Induction in weichen Eisenstaben ermittelt, wobei die Constante durch nur 
eine gleichzeitige Bestimmung mit einem Nadel-Inclinatorium erhalten wor- 
den war ; den Anderungen derselben mit der Zeit wurde vom Verf. in 
derselben Weise Rechnung getragen, wie dies bei der Horizontal-Intensitat 
geschah. £. Solander. 



THE MAGNETIC DECLINATION AND ITS SECULAR VARIATION. 

Weyer, G. D. E.: Die magnetise he Declination und ihre saculare Ver- 
dnderungfur 48 Beobachtungsorter, berechnet als periodische Functionen 
fur jeden einzelnen Ort aus den daselbst angestellten Beobachtungen. 
Nova Acta d. K. Leop. — Carol. Deutsch. Akad. d. Naturf. Bd. 63. No. 3. 
S. 313-397. Halle 1895. 25 X 32 cm ' Repr. pp. 87. 

In this publication Dr. Weyer of Kiel gives the results of his painstaking 
investigations of the secular change of the magnetic declination for the 
following 48 stations: 

Alexandria (Egypt), Ascension I., Astrakhan, Bay St. August in (Nosy Ve* 
Madagascar), Baltimore, Bergen, Berlin, Boston, Bourbon (Reunion), Brest, Brussels* 
Cadiz, Cambridge (U. S. A.), Cartagena, Christiania, Cape Comorin, Conception* 
Capetown, Copenhagen, Cape St. Augustin and vicinity of Pernambuco (Brazil)* 
Danzig, Fernando Noronha, Fort Pr. of Wales, St. Helena, Irkutsk, Jakutsk, Konigs- 
berg, Lisbon, London, Macao, Madeira, Martinique, Mauritius, Nuremburg, New York, 
Paris, St. Petersburg, Plymouth, Quebec, Rio de Janeiro, Rome, Sokatra, Stockholm, 
Tobolsk, Tongatabu, Tornea, Valparaiso and York Factory. 

In two conveniently arranged tables he exhibits the complete data upon 
which the deduced trigonometric expressions are founded, likewise the computed 
elements and results. A graphical representation of the chief characteristics 
of the sec. var. of the mag. decl. at each station is also given. Want of space 
will prevent us from going further into detail, nor can an interesting com- 
parison be given between some of Weyer's results and those of Littlehales, 
whose list of sec. var. expressions (cf. pp. 62 and 89, No. 2) covers nine of 
Weyer's stations. 1 



Notice. — Owing to the amount of excellent matter submitted for publica- 
tion, we have been obliged to exceed our prescribed limit by ten pages. 
Certainly a most healthy and encouraging sign ! 



1 Prepared from an abstract furnished the Journal by Mr. G. Herrle, Chief 
Draughtsman, Hydrographic Office, U. S. A. 



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TERRESTRIAL MAGNETISM 

AN INTERNATIONAL QUARTERLY JOURNAL 

ylEUC tj,. 

VOLUME! OCTOBER, 1896 NUMBER 4 






ISANOMALES ET VARIATIONS S&CULAIRES DES 
COMPOSANTES Y ET X DE LA FORCE MAG- 
N^TIQUE HORIZONTALE POUR L'£POQUE 1857. 

Par le Lieutenan t-G eneral de Tillo. 
Correspondant de l'lnstitut de France. 

Pour rendre complete la serie des cartes des isanomales et 
des variations seculaires de magn£tisme terrestre je viens de 
construire les quatre cartes ci-jointes qui se rapportent a la 
composante occidentale — Y — et k la composante nord — X — 
de la force horizontale. 

C'est seulement gr&ce au concours de M. le docteur Adolphe 
Schmidt de Gotha que j'ai pu executer ce travail, car jusqu'a ce 
jour je n'avais a ma disposition pour les composantes en ques- 
tion que les valeurs se rapportant a l'£poque de 1829 consignees 
dans l'ouvrage de MM. Ermann et Petersen. Les valeurs cal- 
culees par Monsieur A. Schmidt correspondent a l'epoque de 
Tan 1885 ; elles sont basees sur 1' Atlas de magnetisme terrestre 
de M. Neumayer. 

Apr&s avoir calcule les moyennes pour les differentes lati- 
tudes, j'ai construit les cartes des isanomales Y et X pour les 
deux epoques de 1829 et de 1885 et puis j'ai dresse les isano- 
males pour l'epoque moyenne, c'est a dire pour Tan 1857 ; ce 
sont les cartes I et II de cette publication. 

Pour cette m£me epoque (1857) j'ai calculi les variations 
seculaires annuelles et je les ai representees graphiquement sur 
les cartes III et IV ci-jointes (A Yet AX). 

163 



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1 68 A. DE TILLO [Vol. I. No. 4 ] 

En comparant ces cartes I, II, III, et IV avec les cartes de 
mon Atlas on s'apercoit qu'il y a ressemblance frappante entre 
les cartes des isanomales de la declinaison D et que de meme il 
existe une grande ressemblance entre la carte des isanomales de 
la force horizontale — 77 — et la carte des isanomales de la com- 
posante nord de cette force X. On voit aussi que les lignes 
d'£gale variation seculaire ont egalement une grande similitude 
r£ciproque (AZ>et A F; &Het*X). 

Au fond on peut dire qu'il existe deux groupes d'isanomales : 
le premier groupe contient le systeme X, Y, Z? et le second 
groupe contient les elements 77, D, 7, a et il y a grande ressem- 
blance respective entre les isanomales et les lignes d'egale varia- 
tion seculaire. D'un cote ce sont : X % AX; Y, A Y; Z, \Z et 
de l'autre cote : 77, A 77; Z>, AZ>; 7, A 7. 

Les isanomales du potentiel ont la m£me forme que celles de 
la force verticale, seulement la valeur des digressions est deux 
fois plus petite chez le potentiel. 

L'aspect general de toutes les cartes des isanomales confirme 
mon assertion de la division du globe en deux hemispheres dans 
le sens meridional, de sorte que dans Tun de ces hemispheres la 
valeur des elements est plus grande que dans l'autre. Les 
changements seculaires des composantes Y et X s'effectuent 
aussi de maniere a ce que dans une moitie* du globe ils sont 
positifs et dans l'autre partie negatifs. 

Les quatre cartes ci-jointes sont construites d'apres la projec- 
tion equivalente equatoriale de Lambert. Klles font suite aux 
cartes renfermees dans mon Atlas publie par la Societe Imperi- 
ale russe de Geographie pour l'epoque 1859 (1857). La Societe 
Meteorologique de France a publie* dans son Bulletin de l'annee 
1895 cm( l cartes des isanomales magn£tiques pour l'epoque de 
1885 d'apres la projection Mercator. 

1 Force verticale. 
3 Inclinaison. 



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ON THE DISTRIBUTION AND THE SECULAR VARIATION 

, OF TERRESTRIAL MAGNETISM; NO. IV: ON THE 

COMPONENT FIELDS OF THE EARTH'S PERMANENT 

MAGNETISM. 1 

By L. A. Bauer. 

[Abstract.] 

This paper is a continuation of the attempt begun in No. II of 
these researches 9 to localize the centers of disturbance in the Earth's 
permanent magnetic field. In the previous paper (No. II) the normal 
distribution of the Earth's magnetism was taken as that resulting 
from a homogeneous magnetization about the Earth's rotation axis. 
The residual field, among other things, showed a decided polarization 
along the equator. The next logical step then in the breaking up of 
the Earth's complex field into component fields would be to deduct 
from the residual field this one due to the equatorial polarization. 
This has been done in the present paper. 

The normal distribution is now defined as that due to a homoge- 
neous magnetization about an axis inclined to the Earth's axis and 
passing through the Earth's center. This manifestly includes both 
the polar and the equatorial fields referred to above. The position of 
this axis and the value of the magnetic moment due to the magnetiza- 
tion assumed might be obtained in various ways. For the preliminary 
chart which accompanies this paper the position of the axis and the 
value of the magnetic moment have been taken as defined by the 
terms of the first order of the Gaussian analysis. These terms, 
namely, represent that part of the Earth's total magnetic field which- 
can be referred to a homogeneous magnetization about some inclined 
diameter. The values resulting from Dr. Schmidt's computations not 
being conveniently at hand when this investigation was begun, those 
given by the Neumayer-Petersen computation, which, moreover, agree 
very nearly with ^ie former's, were taken for this preliminary trial. 

1 Read before the American Association for the Advancement of Science, Buffalo 
meeting, Aug. 26, 1896. Also presented in abstract, accompanied by a chart, by Mr. 
Watson at the Liverpool meeting of the British Association. A copy of the chart 
was likewise sent to Professor Mascart for the inspection of the members of the 
International Meteorological Conference. 

* Printed in the American Journal of Science, Vol. I, pp. 109-115, 189-204, 314-325. 

169 



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1 7° £• A. BA UER [vol. I, No. 4 ] 

The normal distribution adopted is, accordingly, that resulting from a 
homogeneous magnetization, the axis of which joins the points on the 
Earth's surface whose geographical co-ordinates are 7 8°. 3 N., 6f° .3 W. 
of Gr. and 7 8°. 3 S., 11 2° .7 E., and the magnetic moment of which 
has the value 0.32237 a 3 C. G. S. units, a being the Earth's mean radius. 

Next the values of the normal magnetic potential were computed 
for points lying 20 apart in longitude, beginning with the meridian 
of Greenwich and situated on the parallels of latitude 70 , 6o°, 40 , 
20 north, equator, and 20 , 40 , 6o° south, i. e., for 144 points in all. 
These values were then subtracted from those given by the Neumayer- 
Petersen computation, which represent the Earth's magnetic potential 
to terms of the fourth order. The residual values were plotted and 
the equipotential lines of the residual field drawn. The residual field 
thus obtained would represent the field actually remaining after sub- 
tracting from the Earth's total field that due to homogeneous mag- 
netization, if the Gaussian potential to terms of the fourth order 
embraced the total field, which, as is well known, it does not. 

Therefore, to get more truly the residual field — to deal with 
observed quantities, not with computed ones — I next pursued a 
method analogous to that recently adopted by Riicker. I computed, 
namely, the values of the vertical force, of the northerly and of the 
easterly components due to the assumed normal magnetization for 
points distant 30 in longitude and situated on the parallels 6o°, 40 , 
20 north equator, and 20 , 40 , 6o° south. The computed values were 
subtracted from Schmidt's observed ones, 1 the lines of equal residual 
vertical force were drawn on a map, and the horizontal component due 
alone to the residual magnetization was plotted in direction and magni- 
tude for the points mentioned. Thus the chart accompanying the paper 
was obtained. 2 In conformity with Airy's and Riicker's method of desig- 
nation the north end of a magnetic needle was represented in red, the 
south end in blue.* For the regions, then, over which the north end 
is attracted, the lines of equal residual vertical force were colored red, 
and for the regions where the north end is repelled or the south end 
attracted, colored blue.* The black lines forming the boundaries of 
the red and blue regions join the places where the residual vertical 

1 As given in his Mitteilungen iiber eine neue Berechnung des erdmagnetuckcn 
Potentials, Miinchen, 1895, P* 5 1 * 

a For several copies of the base of this chart (122 x 68 cm) I am indebted to my 
friend, Mr. Littlehales. 

♦ For convenience in the reproduction of the chart in the Journal the color blue 
was changed to black. 



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1 7 2 L. A. BA UER [vol. i, No. 4 ] 

force has the value zero. The scale used to represent the magnitude 
of the horizontal component was : 

i in = 0.3 C. G. S. units, or 

The chart presents a striking appearance. Over the red regions 
the north end (red arrow) points towards the foci of the red lines of 
equal residual vertical force Over the blue regions the south end 
(blue arrow) points towards the foci of the blue lines. These foci 
then we may regard in a certain sense as subordinate magnetic poles, 
those of the red regions being the north-end attracting poles, those of 
the blue the south-end attracting. 1 Whether these subordinate poles 
have a physical existence or are merely the result of our mode of 
decomposition depends in the first instance upon whether the homo- 
geneous magnetization assumed as normal has a physical existence. 
It would seem to me the fact that the Gaussian analysis gives us values 
for the coefficients of the first order terms which so greatly exceed 
those of the remaining terms, implies that a large part, if not 
the whole, of the homogeneous magnetization resulting from these 
first order terms must be given a physical existence, and a distinct 
physical cause must be assigned to it. The writer finds that this sim- 
ple magnetization will on the average for the region considered (6o° 
north to 6o° south) give at least 70 per cent, of the total force of the 
Earth's entire field. 

The next question one might ask is : Is the residual field now 
obtained entirely the result of the heterogeneous geological formation of the 
Earth? That is, is it in the true sense of the word an "anomalous" 
field ? Can none of it be referred to a theoretical component resulting 
from the fact that the Earth rotates about an axis not coinciding 
with the axis of homogeneous magnetization ? As will be seen, there 
are certain strong indications that apparently hold out hope that we 
may be able to still further break up this residual field and that 
consequently we have not yet obtained the purely "anomalous" field. 

By comparing the chart of the residual field with magnetic charts 
of the total field, it is found that the position of the subordinate pole 
(i\Q in China nearly coincides with the center of the oval of westerly 
declination in this region, and furthermore that the subordinate mag- 
netic north pole (JV t ) in the south Atlantic falls in the region of 
greatest disturbance of horizontal intensity (see Neumayer's lines of 

1 For convenience in the reproduction of the chart for the Journal the color blue 
was changed to black. 



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COMPONENT FIELDS OF THE EARTH'S MAGNETISM 1 73 

equal horizontal intensity for 1885). Again, in the region occupied 
by the two foci S t f and S t " great local disturbances are found. So 
can likewise the minor foci be referred to well-known phenomena in 
the distribution, such as for example the peculiar distribution in North 
America (see iV 3 ). Thus the residual field localizes for us the centers 
of the regions of "anomalous" distribution of the Earth's mag- 
netism. 

SUBORDINATE MAGNETIC POLES OR CENTERS OF RESIDUAL FIELD IN 

1885. 



General Loca- 
tion 



I From Lines of Equal Residual 

I Vertical Force 

( Vertical Force 

. Desig - Lat. Long. Obs'd Normal Residual 

nation* (E.ofGr.) (C. G. S.) 



From the 

Equi-residual- 

potentials 

Lat. Long. 

(E.ofGr.) 



S. Atlantic, near 
S. Georgia Is. 

China, near 
Pekin. 

U. S. A., near 
St. Louis. 

Mid-Pacific O., 
near Christ- 
mas I. 

Africa, Kongo 
State. 

Shetland Is. 

S.Pacific C, near 
Dougherty I. 

Bering Sea. 



N, 60 S 330° —.344 —.494 +-I50 

N f 40 N 120 ^-.437 +.306 -M3i 

N 8 40 N 270 +.576 -f -497 +079 

N 4 210 +-o I( > —050 +.060 

S'i 30 —.133 —.017 —.116 

S", 60 N -f.466 +.571 —.105 

S, 60S 240 — .606 — .506 — .too 

S 3 60 N 180 +.501 4-520 —.019 



6o°S 340" 
40 N 120 
40 N 260 

10 N 20 
60 N 
60S 180 



Schuster's 

Diurnal 

Variation Poles 

Lat. Long. 

(E.ofGr.) 



40°S 345° 
40 N 120 



40 N 345 
40 S 120 



From this table it will be seen that the positions of the primary 
centers or foci of the residual field as given by the lines of equipoten- 
tial are nearly the same. Of course theory does not require that they 
coincide. A remarkable coincidence will be noted by comparing the 
positions of the foci of the equipotential lines of the residual field 
with the corresponding ones of the diurnal variation field referred to 
mean Greenwich noon of the summer months of the year 1872, as 
determined by Schuster. The only case where there is a considerable 
difference in the positions of the corresponding foci is in the case of 
S 2 in the southern hemisphere. This may possibly be due to an 
imperfect determination of the equipotential lines of the diurnal field 
in the southern hemisphere. It should be recalled that Schuster at 
the time of his investigation only had records at four stations in the 

♦The letter tells which end of the needle is attracted by the subordinate pole. 
Of course the positions given can only be regarded as approximate. 



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1 74 L. A. BA UER [Vol. I, No. 4 J 

northern hemisphere, and that he had to assume that the field would 
be symmetrical about the equator. Of course the coincidence in the 
position of the foci applies only to mean Greenwich noon. At some 
other time the poles of the two fields would not coincide, since the 
diurnal field shifts to the westward with the time of day, whereas the 
residual field is a permanent one. The point, however, is this: that the 
magnetic system of the residual field has the same general characteris- 
tics of Schuster's diurnal variation fields viz. : a north and a south mag- 
netic pole in each hemisphere, the former lying east of the latter in 
the northern hemisphere and west of it in the southern. Further- 
more, the opposite poles lie roughly north and south of each other in 
the two hemispheres. These poles in both hemispheres are roughly in 
latitude 40 and are distant in longitude by approximately the same 
amount as the poles of the diurnal field. In brief, if the residual field 
were to revolve around the Earth in an east-west direction just as Schuster 
supposes his system of equipotential lines does, it would produce a varia- 
tion of the same character as the diurnal variation. Or, since Schus- 
ter's analysis has shown that the cause of the diurnal variation lies out- 
side the Earth, suppose that the residual field were to induce, in a 
region outside, a magnetic system similar to its own and that the latter 
were to stand still while the Earth rotates beneath it, then would this 
system give rise to a diurnal variation of the same character as the 
observed variation. 

This can be tested in the following way. The diurnal variation of 
the vertical force for a station in the northern hemisphere is of an 
opposite character to that for a point in the southern hemisphere, if 
we refer the variation in each case to the north end of the needle. 
Precisely the same fact obtains with regard to the variation of the ver- 
tical force with respect to longitude for corresponding latitudes in the 
two hemispheres. This is not the case with regard to the homogene- 
ous magnetization field. Here the curve showing the distribution of 
the vertical force along a parallel of latitude is not inverted in cross- 
ing the equator, as in the case of the residual field. The former curve 
has one minimum and one maximum, while the latter, like the diurnal 
variation curve, has two minima and two maxima. 

The magnetic moment of the polar component of the homogene- 
ous magnetization field is nearly five times that of the equatorial com- 
ponent. The residual field gives rise to effects of about the same 
order of magnitude as those due to the latter component. On the 
chart referred to the components of the Earth's horizontal force due 
to the various fields were drawn to scale for the point where the "resid- 



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H 


D 


(C. G. S. 


(north end 


units) 


W.ofN.) 


0.2Q7 


0° 


O.061 


8r 


0.106 


154° 


0.235 


26' 



COMPONENT FIELDS OF THE EARTH* S MAGNETISM 1 75 

ual" component is a maximum, viz., in 20 south latitude and zero 
longitude, /. <r., near St. Helena. It should be noted that this is the 
region where we encounter the largest secular variation changes. 
Referring to my paper on the " Secular Motion of a Free Magnetic 
Needle" it will be seen that in this region we have the secular-motion 
curve of largest area The magnitude (H) and direction (magnetic 
declination D) of the components for this point are as follows : 



Homogeneous Magnetization j J^^™™ 1 

Residual Magnetization Component 
Resultant or Observed " 

The second largest residual component (H = 0.100 C. G. S.) was 
found near Cape Horn. 

Other interesting deductions have been drawn, which, however, 
cannot be presented in a few lines. 1 The paper, moreover, it is hoped, 
will soon be printed in full. 

A careful study of this residual field will probably prove valuable. 
The polar homogeneous magnetization as the Earth performs its 
diurnal rotation will, of course, not induce electric currents in the 
Earth, but simply give rise to a distribution of free electricity. The 
case is, however, different with regard to the equatorial homogeneous 
magnetization, for this part of the Earth's magnetism is un symmetrical 
about the rotation axis. Just what the resultant effect will be — 
whether any part of the residual field obtained above can be referred 
to such a cause — these are questions which, owing to the complex 
structure of the Earth cannot be answered off-hand. They seem to 
the writer questions of vital importance. 

1 It is possible, for example, to ascertain the component of the Earth's magnetism, 
to which the secular variation is mainly to be referred. Again, with regard to earth- 
air electric currents, a curious result has been obtained, viz., the curve showing the 

variation with latitude of I Yd\ Y being the easterly component of the Earth's mag- 
netism, and d\ the elemental arc of longitude, exhihits nearly the same general char- 
acteristics, provided the integral be referred in the northern hemisphere to the north 
end of the magnet and in the southern to the south end, as the curve giving the mean 
atmospheric pressure for various latitudes. We have maxima in latitude 40 N. and 40 
S., and a minimum for 5 N. Notice that the latitudes 40 ° figured prominently in the 
positions of the centers of the residual field. These may be mere coincidences ; never- 
theless, they are worthy of note and merit careful attention. Compare note at end of 
No. II of these researches. 



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ALLGEMEINER AUSDRUCK FUR DIE COEFFICIENTEN 
DER FORMEL FUR DIE ABLENKUXG EINER MAGNET- 
NADEL DURCH EINEN ABLEXKUNGSSTAB IX BELIE- 
BIGER LAGE. 

Von Dr. C. Borgen in Wilhelmshaven. 

Der Ausdruck fiir die Ablenkung einer Magnetnadel durch einen 
Magnet ist bisher meistens nur fiir bestimmt definirte Stellungen des 
letzteren und bis zu einer massigen, aber im allgemeinen ausreichenden 
Grenze der negativen Potenzen der Entfernung zwischen Ablenkungs- 
stab und Nadel abgeleitet worden. So von Gauss* fiir die Lage des 
Ablenkungsstabes in der Horizontal-Ebene durch die Nadel und senk- 
recht zum magnetischen Meridian, von Lamont a fiir diese und ver- 
schiedene andere Lagen, besonders fiir die, seitdem vielfach zur 
Bestimmung der horizontalen Componente der erdmagnetischen 
Intensitat angewandte Stellung des Ablenkungsmagnets senkrecht zur 
Nadel. Von den Beschrankungen der speciellen Lagen des Ablenkungs- 
stabes in der Ebene machten sich frei Riecke, 3 Kowalsky und 
Fritsche, 4 aber auch sie behielten die Beschrankung bei, dass die Axe 
des Magnets in der durch die Nadel gelegten horizontalen Ebene 
liegen solle. Dr. Fritsche ging auch noch einen Schritt weiter und 
fiihrte die Reihen-Entwickelung bis zur Potenz <r -9 , wahrend man sich 
bisher mit der Potenz * -7 begniigt hatte. Im Jahre 1891 veroffent- 
lichte Verfasser s eine Formel fiir die Ablenkung, welche durch einen 
Magnet hervorgebracht wird, dessen Lage im Raume ganz beliebig 
ist und leitete aus derselben die Ausdriicke fiir eine Reihe von Special- 

1 C. F. Gauss : Intensitas vis magneticae terrestris ad mensuram absolutam revocata. 
Wo allerdings auf die Abhangigkeit der einzelnen Glieder von der Vertheilung des 
Magnetismus im Stabe nicht naher eingegangen wird. 

* Lamont: Handbuch des Erdmagnetismus. III. Abschnitt. 

3 Riecke in Poggendorfs Anna/en f Band 149, S. 62 und Wiedemann's Annaltn, 
Bd. VIII, S. 299. 

4 Fritsche : Ueber die Bestimmung der geographischen Lange und Breite und der 
drei Elemente des Erdmagnetismus durch Beobachtungen zu Lande. Hierin auch eine 
Notiz iiber Kowalsky's Arbeit. 

sBbrgen: Ableitung des Ausdruck's fiir die Ablenkung einer Magnetnadel 
durch einen Magnet, dessen Lage im Kaume eine beliebige sein kann. Aus dem 
Archiv der Seewar/e f 1 891, No. 2. 

176 



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ALLGEMEINE ABLENKUNGSFORMEL 1 77 

Fallen ab. Als Grenze der Reihen-Entwickelung wurde wie bei 
Laraont e~ 7 festgehalten. 

Verschiedene Umstande, namentlich Untersuchungen iiber die 
Poldistanz von Magneten, drangten dera Verfasser die Uberzeugung 
auf, dass es unumganglich nothwendig sei bei Bestimmungen dieser 
Art wenigstens noch Glieder der Ordnung r~ 9 zu beriicksichtigen. 
Da die angewendete Methode eine allgemeine Entwickelung der Ablen- 
kungsformei, wenn auch nur fur die Horizontal- Ebene, voraussetzte, 
so wurde versucht, einen allgemeinen Ausdruck fur die Coefficienten 
der Reihen-Entwickelung herzuleiten, um mittels desselben jeden 
beliebigen Coefficienten, dessen Kenntniss etwa erwiinscht sein konnte, 
fur sich allein ermitteln zu konnen. Die Formel (24) in Dr. Fritsche's 
Werk hatte ja ausgereicht, um die Glieder der Ordnung e~ 9 zu beriick- 
sichtigen, es lag dem Verfasser aber daran, sich auch iiber die 
hoheren Glieder ein Urtheil zu verschaffen. Der gefundene Ausdruck 
ist verhaltnissmassig einfach und da vielleicht auch Andere wiinschen 
konnten, fiir irgend eine Ablenkungsart die Reihen-Entwickelung 
weiter fortzusetzen als bisher geschehen ist, so schien es wohl einiges 
Interesse zu haben, denselben hier mitzutheilen. 

Die Abstossung, welche zwei den Magnetismus dm und dm' ent- 
haltende Punkte P s und P H die respective in dem Stabe 6 und in der 
Nadel, ersterer in der Distanz x, letzterer in der Distanz x' von den 
respectiven Mittelpunkten der Elementarmagnete, gelegen sind, auf 
einander ausiiben, wird gegeben durch 

dm dm' 

(AW 9 

dabei moge die Nadel um den Winkel <j> aus dem magnetischen Meri- 
dian abgelenkt sein. 

Zieht man von P s eine Senkrechte P s E n auf die Richtung der 
Nadel, und ist deren Projection in der durch die Nadel gelegte Hori- 
zontal-Ebene P' s £ H , so ist das von dm auf die Nadel in P„ ausgeiibte 
Drehungsmoment gleich 

dm dm' P S E H P' s E n , P f s E H ,. . , 

iprp^-'pTp H 'p^: x ={iw^ x ' im ' /m > 

und das ganze Drehungsmoment der Nadel 

p;e, 



//i 



■ x f dm dm' 



Dieses Drehungsmoment sucht den Nordpol der Nadel zuriickzustossen, 
den Siidpol anzuziehen, also die Nadel dem Meridian zu naheren ; in 

6 Der Kiirze wegen schreibe ich einfach Stab statt AbUnkungsstab. 



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1 7 8 C. BORGEN [Vol. I, No. 4 ] 

deraselben Sinne wirkt aber auch der Erdmagnetisuius rait dera Moment 
x' dm' .Hs\n4> = M , Hs\nit>, 



s 



wenn das magnetische Moment der Nadel mit M' , die horizontale 
Componente des Erdmagnetismus mit H bezeichnet wird. Da die 
Nadel sich in Ruhe befindet, so ist die Summe der auf sie wirkenden 
Krafte gleich Null, und wir erhalten die Ruhegleichung : 

worin die Integrationen iiber die ganze Lange der Magnete ausgedehnt 
werden miissen. 



(i) M'H sin * + ff^^Js *' dm dm ' = ° > 



Wir fiihren nun folgende Bezeichnungen ein : 
e — Entfernung der Mittelpunkte von Nadel und Stab ; 
a = Projection von e auf die Horizontal- Ebene durch die Nadel ; 
f — Hohe des Mittelpunktes des Stabes oberhalb oder unterhalb dieser 

Ebene ; 
x — Entfernung von dm vom Mittelpunkt des Stabes ; 
x' = Entfernung von dm' vom Mittelpunkt der Nadel; 
a — Winkel, welchen die Linie a mit dem magnetischen Meridian bil- 

det; 
p — Winkel, welchen die Projection der Axe des Stabes auf die Ebene 

durch die Nadel mit dem magnetischen Meridian bildet ; 
<f> — Ablenkungs-Winkel der Nadel ; 
if/ — Neigung der magnetischen Axe des Stabes gegen die Verticale. 

Die Winkel a, /J, und ^ werden in der Ebene des Horizonts von 
N durch O, S, und W von o° bis 360 gezahlt, wahrend ^ vom Zenith 
aus nach beiden Seiten von o° bis 180 gerechnet wird, und alle Winkel 
beziehen sich auf die Lage des Nord-Endes von Nadel und Stab; 
endlich soil / positiv sein, wenn der Stab oberhalb, negativ wenn er 
unterhalb der Ebene durch die Nadel liegt. 

Wenn man sich die Figur entwirft, so wird man ohne Schwierig- 
keit ersehen, dass : 

P, E n = a sin (a — <f>) + x sin ^ sin (fi — ^>), 
(P s P n ) 9 = e 7 + x* + x" + 2 fx cos f+2 ax sin + cos (a — $) 

— 2 ax' cos (a — <f>) — 2 xx' sin ^rcos (ft — <£) 

ist, und wenn dies in (1) eingesetzt wird, so ersieht man leicht, dass 



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ALLGEMEINE ABLENKUNGSFORMEL 1 79 

(2) M' H sin <f> = 

— 11 ~ JA> ' * "^ » [**+.*'' + 2/jCCOS^r+ 2 «^Sin^rCOS(a— /3)J 

-\ 2ax' cos (a— <f>) -f- 2*.*' sin ^r cos (/J — <£)! > "~* 



— // 



7£<' + '-*>- 



ist, wenn wir setzen : 

^ = — [ * 2 + *' ' + 2 j /cos ^r -f- a sin ^r cos (a — fi) \x 1 

(3) j = ^,(*' + *''+***) 

2?= — J 2 a jc' cos (a — <f>) -f- 2 xx' sin ^rcos (0 — <f>) 1 
Es ist nun : 

( 4 ) -ri + ^-^i-U-i + i^-i?)-.^^-*)* 

i- -J 2 2 . 4 



2> 



2 2.4 

l) 2. 4 .6....(zr+2)' 2 r+i {A "' 



Hieraus, in Verbindung mit der Form der Werthe von A und B, 
ersieht man, dass das allgemeine Glied der Entwickelung von 
Af' If sin $ die Form 



//■ 



K n n ,x" x'"' dm dm' 



haben wird, und es ist die Aufgabe einen Ausdruck fur K HM . zu finden, 
welcher alle Combinationen von Potenzen von A und B umfasst, wel- 
che ein mit x n x ,n ' multiplicirtes Glied enthalten. Dabei konnen 
jedoch alle Glieder weggelassen werden, in denen n oder n' eine 
gerade Zahl ist, weil das Product x 9 * dm, resp. x ,H dm' , in der Nord- 
und Sudhalfte des betreffenden Magnets entgegengesetztes Vorzeichen 
hat, die Summe der einander entsprechenden Producte und damit 

auch das Integral | x* dm, resp. | x' n dm' , daher gleich Null werden 

muss. Dies gilt allerdings nur unter der Voraussetzung, dass der 
Magnetismus in den Staben syinmetrisch vertheilt ist, was nicht noth- 
wendig immer der Fall zu sein braucht. Diese Glieder werden aber 
immer sehr klein sein und konnen iiberdies durch die Anordnung der 
Beobachtung vollig eliminirt werden. 



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I 80 C. IWRGEN [vol. I. No. 4] 

Durch folgende Erwagungen gelangt man nun leicht zu dem 
gesuchten Ausdruck fiir den allgemeinen Coefficienten K„ n : 

1. Da x' geraeinschaftlicher Factor beider Glieder von B ist, so 
wird jede (ungerade) Potenz von B von 1 bis //' in Verbindung rnit 
noch naher zu bestimmenden Potenzen von A (A° eingeschlossen) 
einen Beitrag zu K HH . liefern. 

2. Nehmen wir die Potenz B p (p < ^ n '), so fragt es sich, welche 

Potenzen von (A — B) in der Entwickelung (4) fiir den Coefficienten 
K H n , zur Anwendung konimen miissen. Dies entscheidet sich durch 
die Ermittelung der hochsten und niedrigsten Potenz von A, welche, 
rait B p multiplicirt, ein x"x' H enthaltendes Glied liefert, denn als- 
dann ist der Exponent r der entsprechenden Potenz von (A — B) 
gleich / plus dera Exponenten von A. 

3. Die hbchste Potenz von A, welche, mit B p multiplicirt, ein 
x"x'"' enthaltendes Glied liefert, ist offenbar diejenige, welche mit 
dem nur x' p enthaltenden Gliede von B p multiplicirt ein Glied mit 

x"x' H ' ergiebt. Dies ist demnach diejenige Potenz von A, welche 

«'-/ 
ein mit x H x' H '~ p multiplicirtes Glied enthalt oder^"* 2 . Im Ex- 
ponenten muss gesetzt werden, weil x' in A nur in der zweiten 

Potenz vorkommt, wahrend fiir ti in diesem Falle nur das Glied 2 gx 
in Frage kommt. Hieraus folgt aber nach (2), dass 

2 2 

der Exponent der hochsten Potenz von (A — B) ist, welche fiir K H „• noch 
in Frage kommen kann. 

4. In ganz gleicher Weise sieht man, dass die niedrigste Potenz von 
A, welche noch in Verbindung mit B p einen Beitrag zu K n%M - liefern 
kann, diejenige ist, welche, mit dem Gliede x p x f/ oder, wenn p > n 
ist, mit x n x ,f multiplicirt, ein Glied x H x' H ' ergiebt. Hier sind daher 

zwei Falle zu unterscheiden, je nachdem / j^ n oder/ > n ist. 

(a) p ti. Urn x H x' n ' zu ergeben muss x p x' p multiplicirt werden 

mit x H ~ p x'"'~ p y d. h. die kleinste Potenz von A, welche in Frage 
3m nit, ist 7 

7 Das Product x n —^x' n '~ /> findet sich in dem Theile von A r —*, welchcr nur von 
1 -f- x' 2 herriihrt, es muss daher im Exponenten sowohl als auch gesetzt 

irden. Da /*, n ' und p ungerade Zahlen sind, so sind ihre Differenzen gerade 
ihlen. 



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ALL GEMEINE A BLENKUNGSFORMEL 1 8 1 

n'—f> , n'—p n +• n — a/ 

^ T" + IT = A a 

und es ist daher der Exponent der klcinsten Potenz von (/4 — i?), wel- 
che B p A " "2 enthait, 

r — ; V P— —z — - • 

2 2 

W / > "• Um .r" #'"' zu ergeben muss #" jc'* multiplicirt werden 

n'—p 

mit .r'"' - ', oder B p ist zu multipliciren mit A a , und der Exponent 
der kleinsten Potenz von (A — B) % welche noch zu berucksichtigen ist, 
wird 

"~~~ +P 



2 2 

Beide Falle lassen sich zusammenfassen, wenn man 
r= H + „'+(p-n) 

2 

setzt und festsetzt, dassp — w = ozu setzen ist, wenn p <n ist. 

5. Wir haben demnach als unteren und oberen Grenzwerth von r 
in der Entwickelung (4) gefunden 

// + >/'+(/-«} 2 »+«'+/ 
r = £ und r=- L ^- . 



Setzen wir aber r — , so haben wir fur m die Grenzwerthe 

2 

/w — - — - und #* -- 

2 2 

zu setzen, von denen der erste der Beschrankung unterliegt, dass der- 
selbe gleich Null zu setzen ist, wenn / < n ist. Innerhalb der Ent- 
wickelung von (A — B) r ist es das Glied 

_ r(r-i)....(r-p+i) 
1 .2 .... p 

welches den gesuchten Beitrag zu K MtH , liefert. Wird dies und der 
eben angefuhrte Werth von r in (4) und (2) eingesetzt, so erhalt man 
die Formel (5) mittels welcher der Coefficient K nn , jedes beliebigen 
x H x'"' durch Producte von Potenzen von A und B ausgedriickt wer- 
den kann. Die weitere Entwickelung ist leicht, wenn man sich die Po- 
tenzen von A und B ein fur alle Mai hinschreibt, wobei man zweck- 
massig in den ersteren zunachst die in (3) eingefuhrte Bezeichnung 

g =/cos 1^ -f- # sin 1^ cos (a— /J) 
beibehalt; man wird sehr rasch iibersehen, welche Glieder in Frage 
kommen. 



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182 



C. BORGEN 



[Vol. I. No. 4 J 






+ 



ft 
ft 






6 

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I 84 C. BORGEN [Vol. I, No. 4] 

Aus (3) ersieht man, dass die Grossen A und B reine Zahlen- 
grossen sind, dasselbe muss daher auch mit der aus Potenzen von A 
und B zusammengesetzten Grosse Fx* x' n ' der Fall sein, und damit 
dies eintritt, muss F den Factor e~ in + "^ enthalten. Da nun nach (5) 
K m% „, = e~ l . F ist, so muss K n% „, den Factor e~ (n + *' + ° enthalten, und 
zwar ist dies die niedrigste negative Potenz von e, welche in K Mt „. vor- 
kommt. Denselben Factor miissen naturgemass alle Glieder enthalten, 
fur welche n -\- n' denselben Werth hat, und man sieht daraus, dass die 
Glieder der Entwickelung von (2) sich in Gruppen theilen lassen, fur 
welche ^- (n + «' +, > gemeinschaftlicher Factor ist, derart, dass nach 
seiner Ausscheidung die K MtU - nur reine Zahlengrossen enthalten, weil 
alle Potenzen von a und / und deren Producte durch Potenzen von e 
von gleicher Ordnung dividirt werden. Aus dieser Betrachtung folgt 
daher, dass, wenn n -\- n' — r+ 1 gesetzt wird, die Glieder mit den 
Factoren K r% x , A" r _ a< 3 . . . . K Zt r- , , K lt r eine solche Gruppe bilden. 

Wenn wir nun Lamont's Bezeichnung 

fx" dm = M n und JV* dm = M' n 

einfuhren, mit der Ausnahme (ebenfalls nach Lamont), dass die mag- 

netischen Momente der Stabe | x dm = M und I x' dm = M f ohne 

Index geschrieben werden, so konnen wir den Ausdruck (2) fur die 
Ablenkung der Nadel, wenn beide Seiten der Gleichung noch durch 
M M' dividirt werden, in folgender Weise schreiben : 

ZJ 

(10) ^sin* = 

VVa- ^j.*- #~M*' , r M,Ml_ AC\ 

Z* \ A '-* jh T *■<—■* MM' - " ^ 3 -~ MM' ~*~ • r M') 

worin demnach alle K den gemeinschaftlichen Factor ^~ (r + a) haben. 
In (9) sind die Ausdnicke fur die Coefficienten bereits nach solchen 
Gruppen geordnet worden. 

M M' 

Was die physikalische Bedeutung von -^, resp. — - t -, angeht, so 

konnen nach den bisherigen Untersuchungen diese Grossen als gerade 
Potenzen der Poldistanz, resp. des Stabes und der Nadel, angesehen 
werden, und zwar ist, wenn wir die Distanz der Pole des Stabes rait 
d s9 diejenige der Nadel mit d H bezeichnen : 

<») f =(*)•"■ j^-(*r 

Unter den Polen eines Magnets sind diejenigen Punkte zu verste- 



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ALLGEMEINE ABLENKUNGSFORMEL 1 85 

hen, in welchen man sich den ganzen Magnetismus jeder Stabhalfte 
vereinigt denken kann, um dieselbe Fernwirkung zu erhalten wie 
durch die wirkliche Vertheilung des Magnetismus im Stabe. Es ist 
nach den bisherigen Untersuchungen des Verfassers ausserst wahr- 
scheinlich, dass d s und d H zwischen 0.80 und 0.81 der Lange der Mag- 
nete betragen werden, und zwar ist bei stark magnetisirten Staben die 
Poldistanz ein kleinerer Bruchtheil der Lange als bei schwach magne- 
tisirten Staben. Dies ist etwas weniger als von F. Kohlrausch 8 gefun- 
den wurde, welcher £ als das Verhaltniss zwischen Poldistanz und 
Lange des Stabes angiebt; es ist aber sehr wahrscheinlich, dass bei 
dieser Bestimmung die hoheren G.lieder nicht geniigend eliminirt sind. 

Um auf bestimmte Falle, bezuglich der Lage des Stabes zur Nadel, 
iiberzugehen, miissen fur /, a, fi und \j/ entsprechende Werthe einge- 
fiihrt werden. Soil die Axe des Magnets horizontal liegen, so ist 
i/, -- 90 zu setzen, und wenn dieselbe in der Horizontal-Ebene durch 
die Nadel liegen soil, so wird /— o und a = e. Die Lage der mag- 
netischen Axe senkrecht zum magnetischen Meridian mit dem Nord- 
ende nach Osten wird ausgedriickt durch ft - 90 und senkrecht zur 
Nadel durch fi — <f> = 90 ° ; ebenso ergiebt a -- 90 ° , resp. a — <f> ~ - 90 ° , 
die Lage des Magnets auf der ostlichen Seite, resp. des Meridians und 
der Nadel, und zwar ist die Verbindungslinie von Stab und Nadel 
senkrect auf dieser ; a~o° und a — <^ = o°, definirt eine solche nord- 
lich von der Nadel im magnetischen Meridian, resp. in der Verlange- 
rung der Nadel uber das Nordende hinaus. 

Es mogen jetzt noch die Ausdrucke fur einige Ablenkungsarten 
hier einen Platz finden. 

1. Erste Gauss' sche Hauptlagc. Ablenkungsmagnet ostlich von 
und senkrecht auf dem magnetischen Meridian, Nordende nach Osten. 
Hier ist zu setzen : /= o, \j/ — 90 , a = p = 90 , a — p = o°, daher : 

A = l - (x> + x' 9 +2ex), B= 2 - sin 4> (x x' + ex' ), 

B' = - 2 cos <f> (xx'+ ex') . 

Da nach (9) B' in alien Gliedern vorkornmt, so ist cos <f> gemein- 
schaftlicher Factor der ganzen rechten Seite von (10) und kann daher 
auf die linke Seite ubertragen werden, indem wir t g <f> statt sin <f> 
schreiben. Ebenso kann durch A^ tl =2 dividirt werden, und wir 
erhalten bis zur Potenz e^, wenn wir, wie iiblich, t 3 als Factor auf die 

8 Nachrichten von der Konigl. Gesell. d. Wiss. und d. Georg-Augusts Un. zu Got- 
fin gen. No. 13, 1 883, S. 40<J. 



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1 86 C. BORGEN [Vol. I, No. 4] 

linke Seite bringen, urn rechts nur reine Zahlengrossen 9 zu behalten : 
(,.) -,.-/,♦=, + _!_, -^ 3^(i-5»»*-)J 

, 1 r j/ 5 J/,^,', . ^ , 45^ s ' 
+ 7'L 3 ^- ,s ^#( I - 5S,n *> + T^ 

(1 — 14 sin * a + 21 sin <f>*) I 
, 1 T M 7 M S M' . . Ja , , 105 

M M ' 
£jj, (i-i 4 sin<ft g +2i sin* 4 ) 

-^Mi-27 sin *>+io5 sin <M - ^ 9 



sin* 6 )] 



+ 



2. Zweite Gauss' sche Hauptlagc. Magnet nordlich von der Nadel 
senkrecht zum magnetischen Meridian. Wenn die Nadel nach Osten 
abgelenkt werden soil, so ist zu setzen :/=o, ^=90°,a=o°, = 270°, 
a— 0= 90°, womit wir erhalten : 

A^ l -(x* + x'*), B= — J*.*'cos *-*.*' sin *J 

B' ie #'sin * -}- x x' cos <f>\ 

Man erhalt daher : 

/ x *H . J r3^i , M' / 15 . J9 \l , 1 Tis 

(,3) ,._/^=,-_|_3_J_6^ T (i--i«n*')J + -[J 

J/ 2 MM' \ 6 ^ / T 3 M' \ 2 

+ __ 8in + ^j__^ 6 _ rlrSr (l --gSlD^) 

3. Erste Lamonfsche Hauptlage. Magnet ostlich von der Nadel 
und senkrecht auf derselben, Ablenkung nach Osten, dann ist /= o, 
ty = 90°, a — <t> = P — <f> - 90 , a — fi = o° und 

9Aus(u)ergiebtsich,dass zrr f -r~ und * a , —J , * — ? , — J- und*«u.s.w. 
v MM M M M M 

von gleicher Ordnung sind. 



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ALLGEMEINE ABLENKUNGSFORMEL 1 87 

Ar= l -(x*+x"+2ex), B=o, B'= 2 -{xx' +ex'). 

Alle Potenzen von B fallen dennach weg und in (9) bleiben nur 
die mit B' allein multiplicirten Glieder iibrig. Das Resultat der Ent- 
wickelung ist : 

M 3 M 3 ' 
MM' 

"•" 8 M')^~ e <\ 4 M~~ 4 MM' "•" 2 MM' 
35^' 



/ > 1 ,^ . ^ , 1 f M, M 3 '\ . 1 ( M i 



4^ / 



+ • • 



4. Zweite Lamonfsche Hauptlage. Magnet nordlich in der Verlan- 
gerung der Nadel, senkrecht auf derselben, Ablenkung nach Osten, 
dann ist/=o, ^ = 90°, o — ^ = o°, /3 — <£= 270 , a — 0= 90 und 

= A -(x' + x"), B=---x', B'=--xx'; 

worn it man erhalt : 

(15) e - nn +-i--{-—-6 W r) + -( JW ~ MM , 

J//x 1 {35 M 7 io 5 M s M 3 ' M 3 M S ' 

^ 5 M'/ e 6 \i6M 2 MM' T 5 MM' 

-•.£)+.... 

5. Endlich moge noch eine Ablenkungsart behandelt werden, 
welche sich besonders zur genauen Bestimmung der Poldistanz von 
Magneten eignet 10 und vom Verfasser zu diesem Zwecke in ziemlich 
ausgedehntem Maasse benutzt worden ist. Die Lage desStabes ist die 
der ersten Lamont'schen Hauptlage, jedoch geht die Verlangerung 
desselben nicht, wie bei dieser, durch die Mitte der Nadel, sondern 
schneidet ihre Verlangerung in einem Abstande = k, wahrend die 
Mitte des Stabes um die Grosse h ostlich von dieser liegt, so dass 
e*=h :i -{-&* ist. In diesem Falle ist /= o, ^=90°, sin (a — <f>) 

= -, cos (a — <£) = -, cos (a — p) = -, f$ — <f> -— 90° und 

A= l -(x° + x" + 2/ix), B= 2 -kx\ B'^ 2 -{xx' +hx'). 

IO B6rgen: Ueber eine neue Methode zur Bestimmung des Polabstandes eines 
Magnets, Annalen der Hydrographies 1891, Februar und Marz Heft. Dieselbe 
Methode wurde gleichzeitig unabhangig von Mr. Blakesley in Philosophical Magazine, 
etc., March 1891, empfohlen, aber leider ist die elegante Form der von diesem gegc- 



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1 88 C. BORGEN [Vol. I. No. 4 J 

Wenn diese Werthe in die Formeln (9) eingesetzt werden, so erhalt 
man, unter Beschrankung bezuglich der rait hoheren Potenzen als e~* 
multiplicirten Glieder auf K lt , und K 9tX , und wenn alles nur durch h 
und e ausgedriickt wird den folgenden Ausdruck : 

( I 6),3_ sln ^ 3 __ I+ _^( + |_ I5 _ + L5_) 

1 M^_ / io5>^ a io5>* 4 \ 

^e^M' \ ^ 2 e* 2 W 

4- L^5/_£5 , 315i a _945^_ 4 , 693 i*\ 
" r ^ 4 J/V I8" 1 " 8 * 9 8 <?*"*" 8 W 

^<r 4 MM' W 2 4 ' 2 ' 4 

3465 >* 6 \ 
4 ' 6 / 
1 ^5' / .- . 525 *** 5355 ^ 4 



1 X ^S / I 

+ ^lr (- I5 + 

, 3465^_ 6 \ 
""*" 8 *«/ 



8 <r* 



I I ^7 / I 35 3i5 >* a . 3465 ^_ 4 
"•"if 6 J/ V ^ 16 4 * 2 "*" 8 <r 4 

_ 3003^ 6435 ^ 8 \ 
4 * 6_t ~ 16 * 8 / 

1 Af Q / 315, 17325^' 75°75^ 4 



128 128 ** 64 * 4 



225225 h* 546975 ^ 8 , 230945 ^'°\ 

"^ 64 <? 6 128 <? 8i ~ 128 e to )' 

M 

Die Methode, diese Gleichung zur Bestimmung von -~ und damit 

nach (11) derjenigen der Poldistanz des Ablenkungsmagnets zu 
benutzen, besteht einfach darin, fur ein gegebenes k dasjenige h zu 
bestimmen, fur welches die Nadel keine Ablenkung erfahrt. Ueber 
die Methode der Beobachtung und Berechnung sowie uber einige 
Ergebnisse von Poldistanzbestimmungen wird in einer spateren 
Nummer der Zeitschrift berichtet werden. 

benen Losung praktisch nicht zu brauchen, weil sie die Lange der abgelenkten Nadel 
ganzlich ausser Acht lasst, obwohl dieselbe eine wesentliche Rolle spielt. Ein von 
Blakesley dort erwahntes Beobachtungs-Resultat, dass die Pole sich mit zunehmender 
Entfernung zwischen Nadel und Stab rasch den Enden des Stabes naherten, verdankt 
seine Entstehung nur dieser Vernachlassigung. 



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ALLGEMEINE ABLEKKUNGSFORMEL 1 89 

Bisher ist vorausgesetzt worden, dass Nadel und Stab Elementar- 
magnete seien, die nur eine Dimension, die Lange, besitzen. Will 
man auf korperliche Magnete iibergehen, so treten gewisse Zusatz- 
glieder auf, welche die Dimensionen der Magnete in Breite und Dicke 
enthalten. Nachstehend mogen, unter Hinweis auf eine Abhandlung 
des Verfassers," diese Zusatzgiieder fur die im Vorhergehenden 
behandelten Ablenkungsarten angegeben werden. 

1 . Parallelepipedische Stabe. Breite 2b, 2b ' ; Dicke 2d, 2d' , wovon die 
accentuirten Buchstaben sich auf die Nadel beziehen. Zu den Aus- 
driicken (12) und (13) fur die erste und zweite Gauss'sche Hauptlage 
sind folgende Glieder hinzuzufiigen : 



(17) 



Hauptlage + 7'[( I5COS **- ,I >^"-^-' /a -' / "] 

I II Gauss'sche . c* r, . . ,,, , ,, . „ -1 

L Hauptlage + — . [( 34 - 45 cos * ') b "+46 '-d'-d "\ 

2. Cylindrisehc Vollmagnete vora Radius r und r' . 
I Gauss'sche 



(.8) 



ausssche , xc "r. 19 . ,, , n 

Hauptlage+^[ (l5COS * I2)r 2r ] 
II Gauss'sche Z ( 'v, .,* ,, , ,1 

Hauptlage + s7' L (33_4SCOS * )r + 3 ' J 



3. Cylindrische Hohlmagnete. Aeusserer Radius r und r', innerer 
Radius r x und r/. 

<,9> 1" °T5SX+H-:[(«-«5«-««r- + , 1 -, + MrM-, 1 ,] 

Der numerische Factor c* ist wenig grosser als i und kann etwa 
gleich i.2 f fur Hohlmagnete jedoch nur = i gesetzt werden. 

Auf die Lamont'schen Hauptlagen geht man uber, wenn man in 
(17), (18), und (19) cos <£-- 1 setzt. 

Fiir die oben unter 5. behandelte Ablenkungsart endlich sind die 
Zusatzgiieder resp. fur parallelepipedische und cylindrische Voll- und 
Hohlmagnete : 

11 Bdrgen : Ueber den Einfluss der korperlichen Dimensionen eines Magnets auf die 
durch denselben aus beliebiger Lage hervorgebrachte Ablenkung einer Nadel. Aus dem 
Archiv der Seewarte, 1895, No. 5. Auch Professor Riecke hat die korperlichen Dimen- 
sionen berucksichtigt. S. die in Anm. 3 erwahnten Abhandlungen. E ben so Dr. 
Fritsche in dem in Anm. 4 genannten Werke, doch stimraen dessen Ausdrucke nicht 
ganz mit denen von Riecke und den obigen uberein. 



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190 



(20) 



C. BORGEN 



[Vol. I. No. 4 j 



c\ 



-- (Ab* + B6' 8 + Cd' + Dd' 2 ) 



worin die Coefficienten folgende Bedeutung haben : 



(21) 



2 ^ a 2 e* 
33 , ^ 2 3*5 ^ 4 

2 2 * 2 



Haben Nadel und Stab nicht dieselbe Gestalt, so braucht man aus 
(17) bis (20) nur die betreffenden Glieder zu entnehrnen und dieselben 
zu combiniren. 



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LETTER TO EDITOR 



MAGNETIC WORK IN AUSTRALIA. 

I am induced to give the following brief account of the magnetic 
work which has been, and is being done at the Melbourne Observa- 
tory, principally on account of an extract from a letter of Professor 
Schuster published in the first number of Terrestrial Magnetism, 
which has led me to believe that the information 1 am about to give 
may not be altogether superfluous. 

Nothing, in fact, has been published in regard to magnetic observa- 
tions in Australia since 1867, beyond records of absolute measure- 
ments. These have appeared regularly in the meteorological records 
of this observatory issued monthly to June 1892 and quarterly since. 

It seems, therefore, opportune to take advantage of the facilities now 
afforded by this new journal for making those who are interested in 
these matters, fully acquainted with the character of our magnetic 
operations, the means we have of carrying them out, and the amount 
of accumulated material in our possession. It will then be fairly 
understood to what extent Australian cooperation may be available for 
future investigations in the common interests of this branch of terres- 
trial physics. 

The labors of Dr. Neumayer in Australia are well known. His 
results, derived from hourly observations of the variations in the mag- 
netic elements, are fully set forth in his admirable work published on 
the subject. 1 Here we learn that Dr. Neumayer commenced the 
systematic registration of hourly readings in 1858, which he continued 
till February 1863 without interruption, these differential observations 
being kept under control by frequent determinations of the absolute 
values of the magnetic elements, about 40 in all, or at the rate of 8 
per year. 

The main purpose was to accurately determine the declination, 
horizontal and vertical component for a fixed epoch, and to construct 
by means of the hourly observations, curves and expressions repre- 
senting the periodical variations, and the laws by which they are gov- 

1 Discussion 0/ the Meteorological and Magnetical Observations made at the Flagstaff 
Observatory, Melbourne. J. Schneider, Mannheim, 1867. 

191 



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1 9 2 P. BARA CCHI [Vol. I , No. 4 J 

erned. The task was executed with astonishing alacrity, and its 
expectations were completely fulfilled. 

Dr. Neumayer during the same period also undertook and com- 
pleted a magnetic survey of the Colony of Victoria, determining the 
magnetic elements of some 235 stations. 1 The only systematic obser- 
vations on terrestrial magnetism recorded in Australia previous to 1858 
are those made at Hobart in the Colony of Tasmania in 1846-50. 

The publications dealing with all magnetic work done in these 
parts of the world to the end of 1863 have long been in the hands of 
scientific men, and nothing more remains to be said here in that respect. 
It has already been remarked that very little was published in subse- 
quent years concerning Australian magnetic operations, and this is no 
doubt the reason why it has been supposed in some quarters that this 
class of work had been discontinued. Such, however, is not the case. 
After Dr. Neumayer left Australia in 1864, Mr. R. L. J. Ellery, then 
Government Astronomer to the Colony of Victoria, assumed the 
direction of the Magnetic Department, this having been some months 
previously amalgamated with the Astronomical Observatory at Mel- 
bourne. 

The hourly observations which had been suspended since March 
1863, were not systematically resumed ; but the absolute measurements 
were continued from time to time with the same instruments and 
methods as in Dr. Neumayer's time until the end of 1865. In Janu- 
ary 1866, the old instruments were superseded and replaced by a unifi- 
lar magnetometer (Kew pattern) and a Barrow dip circle, with which 
the determinations of absolute values of the magnetic elements have 
been made ever since, on an average ten times in each year. 

Early in 1867, the observatory obtained a complete set of self- 
registering magnetographs similar in all respects to those employed at 
the Kew Observatory, and described in the Report of the British Asso- 
ciation for 1859. These instruments arrived in Melbourne in April 
1867, and were mounted shortly after. They have been at work con- 
tinuously since then, with only one serious interruption of three 
months in 1877, when a new building was erected for their permanent 
location. Other short stoppages have occurred from time to time 
owing to accidents or cleaning and repairing, amounting to a few 
hours at most in each case, though once for a few days, when the mir- 
rors had to be resilvered. All magnetic operations since 1864, were 

1 An account of this survey, the merits of which are worthy of the highest praise, 
is given in Results of the Magnetic Survey of the Colony of Victoria, J. Schneider, 
1869. 



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MA GNETIC WORK IN A USTRALIA 1 93 

carried out by Mr. Carl Moerlin under the direction of Mr. R. L. J. 
Ellery until June 1892, and from that date to the present time, I have 
had charge of the work. 

The system adopted in the making of the observations and in their 
reduction has always been the same throughout, and is in accordance 
with the rules given in the Report of the British Association cited above. 

The unifilar magnetometer (Kew pattern) and the Barrow dip cir- 
cle, are mounted on stone piers in a small wooden house at a distance 
of about 200 feet from the nearest building, from which position sev- 
eral distant objects whose true bearings are known, can be observed at 
any time for determining the zero reading of the azimuth circle, in 
observations of the magnetic declination. There is no necessity to 
give details of these instruments ; for they have been fully described 
in the Reports of the British Association and elsewhere. I shall there- 
fore mention simply their principal dimensions and constants. The 
circle of the unifilar magnetometer is d Y / 2 inches in diameter and 
reads to 20 seconds. The magnets i&z and \%b are hollow cylinders 
3.9 inches in length, weighing respectively 675 and 641 grains, and 
having a collimating lens at one end and a scale on glass at the other, 
the angular value of one division being 2 '.25. 

The magnet i8£, serves for declination observations, and i8a is 
the vibrating magnet and also the deflector used in conjunction with 
the suspended magnet 18^ in deflecting observations. This latter is a 
cylinder 3 inches long, with mirror attached. Magnet 180 is provided 
with appendages for insertion of the inertia cylinder, which weighs 
108 1 grains. 

For the deflecting magnet, the correction to 38 F. is : 
0.0001362 (t — 38) -fo.000000636 (t — 38)* 
in which t is the observed temperature. 

The induction coefficient fi is 0.0002203, and log 7? Kat 6o° F. = 
1. 616692. 

In the dip instrument, the circles are 6 inches in diameter and 
read to single minutes. 

A complete determination occupies about four hours, and consists 
of a double set of 8 deflections, with the deflecting magnet placed at 
distances of 1.0 and 1.3 feet; a double set of vibrations each including 
ten independent observations of the time of 100 vibrations; observa- 
tions for torsion ; four to six readings for declination, and two sets of 
32 readings made with two different needles, for dip. The table 
appended is an abstract of results, from observations made on Decern 
ber 30, 1895. 



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I 94 P. PARA CCHI [Vol. I. No. 4 ] 



Table Showing Results of Observations for the Absolute 
Values of the Magnetic Elements. 

Melbourne Observatory, December 30, 1895. 

Deflections. 

First Set Second Set 

Melbourne Mean Time (civil date) o, h 23" a.m. 9 h 44™ a.m. 
Temperature, Fah't 67°. 5 6V.4 
Observed Deflection at a distance of 1.0 feet 12" 58' 2' 12* 57' 45' 
•• •« «• " «• •« 1.3 feet 5 52 20 5 52 00 
log. ™ ■•" •« "1.0 feet 9-Q5354 9.05355 
1.3 feet 9-05364 9.05339 

(m= magnetic moment of deflecting magnet ; X=hor'l comp't.) 

Vibrations. 

First Set Second Set 

Melbourne Mean Time (civil date) io h 43 m a.m. io h 55 1 " a.m. 

Temperature, Fah't 69".6 7i°.2 

Period of One Vibration 3*-7732 3 S 7740 

log mX 0.46444 0.4643S 

m= 0.57408 0.57408 

Declination. 
At 1 i h 34 m a.m. Observed East Declination (mean of 6 readings) 8 C 16' 46' 

Dip. 

At n h 54 m a.m. \ By Needle No. 3, Dover 

Melbourne Mean Time \ By. Needle No. 4, Dover 

Absolute Measures. 

Horizontal Component 

Vertical 

Total Force 



67' 
67 


20' 4* 
19 38 


B. A. Units 
(Foot, Grain, Sec) 

5.O7488 


CG.S. 
0.23399 


I2.I502 


O.56023 


13.1675 


O.607M 



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MAGNETIC WORK IN AUSTRALIA 195 

The magnetographs are located in the basement of a masonry 
house also detached from other buildings. They stand on stone piers 
about 3 feet below the level of the ground. The locality is admirably 
adapted for the purpose, being in the center of a large park, a mile 
away from the city, on a hill of " Silurian formation covered with cap- 
pings of tertiary deposits ; " and there has never been any apprehension, 
or reason to fear that the action of these instruments might have been 
seriously disturbed by local circumstances. 

Photographic traces representing the oscillations of the declina- 
tion, and horizontal and vertical component, are secured by means of 
these instruments. The traces are marked on bromide paper and 
developed by the iron process. The cylinders on which the papers 
are wound being 5 inches in diameter, and one revolution taking place 
in 24 hours, the daily curves are 15.7 inches in length, or a length of 
abscissa of 0.65 inches represents one hour. Two days' curves are 
marked on each sheet. 

Besides the photographic registrations, the position of the magnets 
can be observed at any time by telescopes provided with scales 10 
inches in length and divided into 500 parts, reading by estimation to 
0.002 inches or 0.05 mtD . Gas light is used for the production of the 
photographic traces. The maximum and minimum temperature of 
the room is observed every day ; the scale readings are always recorded 
twice daily ; and the readings of the base lines are frequently taken to 
check the rigidity of the telescopes and scales. The absolute values of 
these base lines are deduced from the observations made with the uni- 
filar magnetometer and Barrow dip circle, and thus a control over the 
instruments is maintained. 

The determinations of the value of one division of the scales and 
of one inch ordinate on the photographic curves are made from time 
to time. The last values were obtained in March last and are as 
follows: 

Value of one Value of one 

division of scale inch ordinate 

Declination ' .822 28 ' .947 

Horizontal Force 0.000324 (in parts of force) 0.011275 (in parts of force) 

Vertical Force 0.000199 ( " ) 0.009777 ( " ) 

These coefficients are determined by the deflection method. The 
accumulation of the daily traces extends over a continuous period of 
twenty-nine years. The commencement and end of each curve, the 
corresponding reading of the scales and the absolute value of the base 
lines, are available for the complete reduction of the records. 



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1 96 P. BA R. 1 CCIff [Vol. I, No. 4] 

So far these daily curves were only cursorily examined on the 
occasion of remarkable disturbances, and sometimes used for reducing 
absolute measurements to the mean of the day ; beyond this no other 
information has been systematically derived. 

We have felt for a long time that a thorough discussion of this 
large quantity of material ought to be undertaken. My predecessor 
recognized this necessity ; but owing to the meteorological service 
increasing every year, the meridian astrophotographic, and other astro- 
nomical work claiming the closest attention, and the multitude of other 
scientific obligations inherent to the national character of the institu- 
tion, it was not found possible to deal thoroughly with the magnetic 
records, and in later years we were often forced to consider the desir- 
ability of discontinuing this work altogether. Now the conditions are 
much worse, as the staff has been diminished during the last four years 
by the retirement of three of its members besides Mr. Ellery, while the 
amount of work generally has as far as possible been kept at the same 
standard. But now as before the strong reason for keeping up the 
magnetic registrations, is that at no other place in Australasia but the 
Melbourne Observatory, has this class of work ever been undertaken, 
excepting the series of observations made at Hobart, Tasmania, more 
than half a century ago. 

Naturally I feel that it would be of little value to go on collecting 
records, if we cannot make use of them ; but the plan for submitting 
all the data to a thorough discussion is under consideration, and I 
only await the opportunity of obtaining from the government some 
extra assistance to carry it out. 

P. Baracchi. 

Melbourne Observatory, 
May 19, 1S96. 



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NOTES 

The delay in the appearance of this number has been caused partly by the 
absence from Chicago of the editor who is at present engaged on the work 
referred to below and partly by the preparation of the colored plates, the 
expenses of which have been borne by the authors themselves. It has like- 
wise not been possible to prepare notes on current events. 



Magnetic Observations en route to Greenland. Mr. G. R. Putnam, Assist- 
ant in the U. S. Coast and Goedetic Survey, accompanied the expedition to 
the west coast of Greenland, under the leadership of Professor A. E. Burton, 
of the Massachusetts Institute of Technology, for the purpose of making mag- 
netic and pendulum observations. A complete instrumenal outfit belonging 
to the Coast and Geodetic Survey was used in the work. The party sailed 
from Sydney, Cape Breton, on July 16, 1896, with Lieut. R. E. Peary, U. S. N., 
on the steamer " Hope," and returning reached Sydney on September 26, 
1896. Magnetic observations, including declination, dip and intensity meas- 
urements, were made by Mr. Putnam at Halifax, Nova Scotia, Sydney, Cape 
Breton (two stations), Turnavic, Labrador, Ashe Inlet, Hudson Straits, God- 
haven, Greenland (two stations going and returning), Umanak, Greenland, 
and Niautilik, Cumberland Sound. Umanak in latitude 70 41 ' is the most 
northern of these points, but Ashe Inlet and Niautilik are nearer the mag- 
netic pole. The observations will be published in the near future. 



THE MAGNETIC SURVEY OF MARYLAND. 

The Maryland Geological Survey, in an endeavor to make its work fun- 
damental and at the same time of the greatest value to the material interests 
of the state, has taken up, in its preliminary investigations, a thorough study 
of the magnetic conditions affecting that portion of the Earth's crust within 
the borders of Maryland. In addition to the importance of this work upon 
the future observations and determinations of the great rockmasses con- 
tained within the state, these investigations will be of immediate practical 
benefit to all land surveyors and from that standpoint alone justify the under- 
taking. 

The investigations are being conducted by L. A. Bauer, under the direc- 
tion of the state geologist, Professor VV. Bullock Clark, in charge of the 
Geological Department of the Johns Hopkins University. By the courtesy 
of the Secretary of the Treasury, one of the new and improved instrumental 
outfits of the Coast and Geodetic Survey has been placed at the disposal of the 
Geological Survey of Maryland during the summer and autumn months of 
the present year, an arrangement which has alone made the work possible. 
At the same time the American Association for the Advancement of Science 
has allotted to Mr. Bauer a sum of money to aid in carrying on the investiga- 
tions. 

Although the importance of magnetic surveys appears to be generally 
recognized, no systematic work of this kind has been undertaken in this 
country by the separate states, with the present exception. Professor F. E. 
Nipher, in carrying on his Magnetic Survey of Missouri during the years 
1878-83, embracing on the average one station to every 435 square miles, 
was dependent wholly upon private contributions. 

197 



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198 REVIEWS [vol. I. No. 4 ] 

Observations of the three magnetic elements have been made at about 
forty stations, averaging thus one station to every 250 square miles. There 
are, moreover, about thirty points, where observations were made, between 
the years 1845 anc * l &9$* Dv tne United States Coast and Geodetic Survey 
and otherwise. A few of these have been re-occupied and it is hoped to 
re-observe at all of them. The Survey will then ultimately average one sta- 
tion to about 140 square miles, thus equaling in detail that of Rucker and 
Thorpe in the British Isles. 

There is probably 110 state in this country that presents, within so small 
an area, such a variety of geological formations, as Maryland. It is then 
peculiarly fortunate that a detailed magnetic survey has been undertaken in 
this state and simultaneously and in connection with the Geological Survey. 
It is hoped that other states will soon follow the example set by Maryland. 

Owing to the warm and appreciative interest of the state geologist, it will 
be possible to issue a report of the work some time this winter. 



REVIEWS. 

MAGNETIC OBSERVATIONS IN ITALY. 

Missure assolute degli Elementi del Magnetismo Terrestre eseguite in Italia 
negli anni 1888 e i88g t dal Dorr. Luigi Palazzo, assislente ftsico 
deir Ufficio Centrale Meteorologico e Geodinamico. Roma, 1895. Fol. 
pp. 151. 

This publication is an extract from the Annals of the Central Office for 
Meteorology and Geodynamics, Vol. XVI, Part I, 1894. It is divided into 
two parts, the first one dealing with the method of observation and the deter- 
mination of the instrumental constants ; the second and larger one contains 
part of the record and the results at twenty-two stations in Italy occupied 
between the epochs 1888.8 and 1889.7 Similar work had previously been 
carried out by Professor Chistoni and whose methods were followed by Dr. 
Palazzo. 

The instruments employed in the surveys of 1888 and 1889 were, (1) a 
magnetometer after the Kew pattern, but afterwards greatly altered, this is 
the same instrument which had been used the year before by Chistoni ; (2) 
an inclinometer by Dover ; (3) a box chronometer beating half -seconds, also 
a pocket chronometer showing Rome mean time ; (4) a prismatic compass 
by Negretti and Zambra. The party was provided with a tent. In selecting 
a station much attention was bestowed to the examination of the soil and 
rocks as well as to all other causes suspected of possible magnetic disturb- 
ing influence. The geographic positions of the stations were taken from the 
topographic map of Italy. For the determination of the azimuth of the 
mark and for local time the Sun was observed with a theodolite ; the effects 
of small errors in polar distance, in latitude and in altitude on the azimuth 
are investigated, likewise any errors that may arise from imperfect instru- 
mental adjustments. The same care is bestowed on the magnetic part of the 
instruments, on the determination of their constants, and the possible influ- 
ence on the results of any outstanding defect in the various operations. This 
investigation into sources of error and of their individual magnitude forms 
quite a distinctive feature of the publication. In the absence of other means 
to reduce the results to the mean value of the day, frequent observations 
were made at each station extending over 2 or 3 days, and in case of the 



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REVIEWS 199 

declination observations were made at intervals of 15 or 20 minutes between 
the morning hours, 9 -.30 and 1 1 : 30. 

In Part II we have given for each of the twenty-two stations a descrip- 
tion of the place, a reference to the azimuth mark, a note of the geological 
features of the locality, the geographical position of the place, and the detail 
and results of the magnetic observations. The work concludes with a col- 
lection of results in tabular form giving the resulting declinations, dips, and 
the horizontal and the vertical components of the force, together with the 
values of the total force, all expressed in C. G. S. units, for the time of obser- 
vation. C. A. Schott. 

THE MAGNETIC RESULTS OF THE VOYAGE OF H. M. S. 
PENGUIN, 1890-93. 

In June 1895 Captain E. W. Creak, R. N., F. R. S., presented to the 
Royal Society of London a paper giving the results obtained by the reduc- 
tion of observations of the magnetic elements made by the officers of H. 
M. surveying vessel Penguin on the north, west, and south coasts of Aus- 
tralia, at Hongkong, and at the intermediate stations between England and 
the East occupied by the Challenger expedition. 

The instruments used were : 

1. Unifilar Magnetometer, No. 25, by ) ~ . , ^ , 

pn . 4 • ? . ' J J { For absolute observations 

Elliot, with two magnets. \ 1 , 

2. Barrow's Dip Circle. ) on lana * 

3. A Fox Dip and Intensity Appar- ( For relative observations 

atus, No. C. 10. f on board ship. 

4. An Admiralty Standard Com- / For observations ashore 

pass. \ and afloat. 

To secure reliability in the observed values, the instruments for absolute 
observations were compared with the Kew standards before the beginning of 
the cruise and again after its completion ; and with the magnetic instruments 
in the observatories at Hongkong and Melbourne during the cruise. The 
results are printed in detail in the Phil. Trans. Roy. Soc. % Vol. 187 (1896) 

A, pp. 345-381. 

An important part of the magnetic work accomplished by the officers of 
the Penguin, and one of much value to navigation, consists of a careful sur- 
vey of the region of magnetic disturbances that had previously been discov- 
ered near Port Walcott, in N. W. Australia. From this it was found that, 
at a point situated 2.155 miles N. 78" E. (true) from the southern end of 
Bezout Island, there exists, in the land which here lies eighty-two feet below 
the surface of the sea, a source of magnetic disturbance, causing the 
magnetic elements to vary from their normal values by the amounts here set 
forth, the intensities being expressed presumably in metric (Gaussian) units : 

Declination Dip Horizontal Force Vertical Force 

26 W. to 56* E. — 29 +1.04 to — 1.92 — 4.44 to +0.32 
on N. side on S. side ... on X. side on S. side 

Going outward from this point the values gradually assume their normal 
amounts. The general direction of the area within which there is disturb- 
ance is N. 50 E. (true), and its approximate dimensions are 3 by 1 % miles. 

Neither a geological examination of exposed cliffs nor anything to be 
found in a collection of specimens of rock and sand in the region of Port 
Walcott could afford an explanation of the cause of the disturbances, although 
the seat of them was determined to be in the land underlying the sea. 

G. VV. LlTTLEHALES. 



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200 REVIEWS [vol. I, No. 4) 

COMPARISON OF THE MAGNETIC INSTRUMENTS IN THE 
OBSERVATORIES OF THE BRITISH ISLES. 

The committee appointed by the British Association for the purpose of 
comparing the magnetic instruments in the different observatories of the 
United Kingdom, presented a report to Section A of the Association, at its 
Liverpool meeting in 1896, showing that the comparison of the Kew stand- 
ards with the instruments in use at Falmouth, Stonyhurst, and Valentia was 
carried out, during the summer of 1895, by Professor A. W. Rucker and Mr. 
W. Watson. 

At Greenwich no comparison could be made because the magnetic sur- 
roundings of the declination needle in use there made it necessary, in order 
to be certain of the accuracy of the results, to place the comparing instru- 
ment on the same site, but the peculiar form of the Greenwich needle makes 
it impossible to put another in its place. 

The magnetometer and dip circle used in the recent magnetic survey of 
the United Kingdom were transported from place to place for the purpose of 
making the comparisons, having been compared with the standard instru- 
ments at Kew Observatory in July, before setting out, and again in October 
upon the completion of the work at the other observatories. The compar- 
isons were made as follows : "LetCo and C be the readings of the self- 
registering instruments at the time when the value of the element was deter- 
mined by the Kew standard (K) and No. 70, the comparing magnetometer, 
(S), respectively. Then K— C = Z and S— C = Z are the values of the 
zero-line of the self-registering instrument according to the two observations. 
But, if the observation with No. 70 has been made at the same instant as 
that with the Kew standard, and if the zero-line remained unaltered in the 
interval which actually occurred between the two experiments, the simul- 
taneous values of the element given by the two instruments would have been 
K and S = S +C -C; therefore, K - S = K — C — (S' — C) =Z — Z." 

A summary of these results is given in this table, which is to be read from 
left to right, thus : The declination given by the Kew standard = that given 
by the Falmouth instrument — 0.8. 



Kew 



DISTRIBUTION OF MAGNETISM IN SOUTHERN SWEDEN. 

Carlheim-GyllenskOld, V.: Me'moire sur le Magnitisme Terrestre dans 
ia Suede Meridionals Kongl. Svenska Vetenskaps-Akademiens Hand- 
lingar. Bandet 27, No. 7. Stockholm, 1895, 4 , 93 pp., 5 plates. 

In the important work before us the author has attempted, with the aid 
of old and new observations, to give for the epoch September 1, 1892, a rep- 
resentation of the actual distribution of the magnetic elements in southern 
Sweden. It is unfortunate, as the author himself has recognized, that 
Angstrom's numerous observations were not at his command for this purpose. 
The observation data, which in general were unreduced, had to be corrected 
first for the daily and the secular variation. As, sad to say, there is no 
magnetic observatory provided with self-registering instruments in Sweden, 
use had to be made in the reduction to mean of day of the term observations 



Falmouth 


Stonyhurst 


Valentia 


-0 .8 


-f I'. I 


— o'.o Declination 


-1 .6 


+ 2 .2 


— 1 .8 Dip 


— .00018 


— .00006 


+ .00029 Horizontal Force 
(C. G. S. units) 

G. VV. LlTTLEHALES. 



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REVIEWS 201 

i st and 15th of month) made during the polar year 1882-3. As the diurnal 
variation varies with place and date the correction thus obtained was, of 
course, only approximate. Furthermore, to reduce the inclination to mean 
of day, the data of the Pawlowsk Observatory had to be utilized. 

To obtain the secular-variation correction, formulae were established for 
places where long series of observations were obtainable, viz., Copenhagen, 
Gothenburg, Christiania, Stockholm, Upsala and Haparanda. At first a 
quadratic parabolic formula was used to represent the horizontal-intensity 
observations, but as it was found that the coefficient of the second term was 
very small for all the stations with the exception of Upsala, 1 a simple linear 
formula was employed. Next the time coefficient was expressed as a linear 

function of the latitude, the final formula for the annual change . , in 

units of the fifth decimal C. G. S. being, 

— = 13.44-0.647(0- 59°-i3) + 1-32 (kcos0- i°.43). 

where <t> = latitude and * = longitude, reckoned west from Stockholm. 

For the secular variation of the declination a four-term series (argument 
time to fourth degree) was employed. As it was found that the coefficients 
of the different terms for the various places were nearly alike, the final formula 
used was obtained by taking the mean coefficient for each term, viz.: 

AZ?= [0.3778] (/— 1800) -f [9.0588 «] (/•— 1800) * 

+ I 5-9595 *] ('— 1800)3+ [4.7021] (/— 1800)*, 

the bracketed quantities being the logarithms of the coefficients. This close 
agreement of the coefficients is a matter of some surprise for, a prion, one 
might expect that, since the product Htg&D is an intensity component of the 

same kind as . , it should likewise vary with locality and according to 

somewhat the same laws as those of the latter component. 

For the representation of the secular variation of the inclination a three- 
term series (argument time to third degree) was used. In this case, how- 
ever, the coefficients were found to be dependent upon geographical position. 
But since the observations were insufficient to permit expressing the 
coefficients of the higher terms as functions of <f> and *, the mean values 
simply were taken and only the coefficient of the first term was treated as a 
linear function of and *. The final formula obtained was : 

A i — [ — 1 .437 -}-o'.i2Q (4> — 6o°) -- o'.oioi k] t -i- 1 '.683.io- J T a 

-+- .304.10-^3, 

where the time, t, is reckoned from the year 1850. It should be mentioned 
that the observations, before the computation, were combined into eleven-year 
means, in order to eliminate as far as possible the sun-spot and polar-light 
period. 

In this manner all available observations were reduced to the same epoch, 
giving 

Declinations at 278 stations, or one to every 532 km *. 

Horizontal intensities at 336 " ** " 44! " 

Inclinations at 233 " " " 635 " 

* This fact appears to be of some interest since there are considerable local dis- 
turbances at this place which most likely exert an influence upon the progress of the 
secular variation. Of course it is also possible that this case of exception is* partly 
accidental, since the series of observations extends back onlv to 1869. 



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202 REVIEWS [Vol. I, No. 4 ] 

The isomagnetic lines of all three elements were next drawn without 
elimination of local disturbances. As was to be expected, these curves pre- 
sented a most complicated appearance, in the case of the isogonic chart, for 
example, there are no less than 35 isolated closed areas. The author next 
proceeds to a mathematical discussion computing first the surface density 
requisite to produce the observed distribution. This was done with the aid of 
Gauss's formula Allgemeine Lehrsatze % etc., § 35) viz.: 

-4 * * = j,(Po -r 3* -f SP* + 7P3+ ) 

or 

where P= Earth's mean radius, U= Earth's magnetic potential, and V = 
vertical intensity. U can be obtained to within a constant term by integra- 
tion of the equation : 

d 17= — H cos e ds y 

ds being the arc element of the Earth's surface and e the angle it makes with 
the magnetic meridian. The surface density 9 obtained thus, reckoned from 
an arbitrary zero point, the author regards as the sum of two quantities V and 
a ' ' , of which the first is to be referred to the normal distribution of the 
Earth's magnetism and for the area considered can be taken as linearly vari- 
able with geographical position, viz.: 

a = tfoo + a 10 (<p — O ) -f a ox (k — k q ) x 

By the method of least squares V was obtained and then the residuals 
9" =<r — 9' were derived ; <r" was then to be regarded as representing the 
surface density of the disturbing magnetic masses. After representing 
cartographically in colors the distribution of the disturbance surface density, 
the potential, U, was treated in a similar manner except that in the computa- 
tian of U lt of the normal distribution terms of the second order likewise had, 
of course, to betaken into account. The chart of the equipotential lines of 
the disturbing masses, as was to be expected, exhibited great similarity to 
that of the distribution of <r ', so that, as a rule, a maximum of south-pole 
magnetism on the latter chart corresponded to a minimum potential on the 
former and vice versa — the two methods of representation thus mutually 
checking each other. Again, both charts, as far as the positions of the max- 
ima and minima are concerned, agree, on the whole, very well with that 
which might be expected from the distribution of the iron bearing rocks. For 
details we must refer to the original. The author finally raises the question 
whether the magnetic rocks have been magnetized by induction in the Earth's 
field, or whether they contain permanent magnetism, in which latter case their 
magnetism can be considered to be an integral part of that of the Earth's. 
In the first case, one would expect that the maxima of the south-pole mag- 
netism would be more sharply defined and distributed over a much smaller 
area than those of the opposite magnetism, but the author finds that the 
ratio of the areas of positive and negative disturbance surface density is as 
7:6, or nearly unity, which apparently would declare in favor of the second 
hypothesis. It seems to the reviewer, however, that this can only have been 
the result of including in the computation the surface area of the surround- 
ing ocean, and that, therefore, this question must still be regarded as an open 
one. E. Solander. 

1 The last term would really have to be further multiplied by cos <p. 



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REVIEWS 203 

Sella, Alfonso : Misure relative delta componente horizontale del tnagne- 
tismo terrestre sul Monte Rosa, a Biella ed a Roma. Roma, 1896. 

Cet opuscule se rapporteades mesurements ex6cut6 par l'auteuren 1893 
et 1894 aux points suivants : 

Sur le Mt. Rosa : glacier du Grenz (punta Gnifetti) a une hauteur de 
4300™ ; glacier de Garstelet, pr£ aux environs de Gressoney la Trinite". 

A Biella : haute plaine d'alluvions alpines a la gauche du torrent Cervo. 

A Rome (en 1894 seulement) : la Farnesina, % de"ja e'tudie'e en detail par M. 
Folgheraiter. II se servit d'une barre de i6 cra de longeur pesant 40^, 
aimantle il y a vingt ans, ce qui garantissait la Constance du moment 
magnltique. Comme durde d'une oscillation complete on trouve : 



En 1893. 




En 1894. 




Biella - 


■ 1 1,6708 sec. 


Biella ... 


- 1 1,6766 sec. 


Punta Gnifetti 


u,7346 " 


Rome - - - - 


IM433 " 


Glacier Garstelet 


- 11,7228 " 


Punta Gnifetti - 


- ii,7338 " 


Gressoney la Trinite* 


11,8821 " 


Glacier Garstelet - 


11,7220 " 






Gressoney la Trinite" - 


- 11,8885 " 



Ce qui donne comme rapport entre la composante horizontale (H B ) de 
Biella et celle du sommet de Monte Rosa, Punta Gniffetti (ff G ) 

H B :H G = 1,0104. 

La comparaison entre Novara et plusieures stations pres du lac de Lucerne 
dormant une difference moyenne de 0.00032 par minute de latitude pour la 
dite composante horizontale, il en r£sulte que sur les 21 minutes de distance 
entre Biella et Punta Gnifetti Ton devrait avoir ; 

H B :H G = 1,0067 

au lieu de la valeur observed, ce qui laisse entrevoir pour H une diminution 
de 0,001 par kilometre de hauteur ; la difference de niveau des stations 6tant 
de 4000™ a peu pres. Du reste Tauteur fait remarquer la nature fortement 
magn6tique des rochers serpentins et amphibolitiques trouv£s sur le terrain. 

P. W. 



PUBLICATIONS. 1 



Batavia. Observations made at the Magnetic al and Meteorological Observatory 
during the year 1894. Vol. XVII. 1894. Batavia, 1895. 26x36"". Pp.233. 
[Contains the customary observations and results for 1894 and an Appendix "On 
Lunar Diurnal Variation of Magnetic Elements at Batavia, 1883-1894, Part L"]. 

Borgen, C. Ueber den Einfluss der korperlichen Dimensionen eines Magnets auf 
die durch denselben aus beliebiger Lage hervorgebrachte Ablenkung einer Nadel. 
Aus dem Archiv der deutschen Seewarte, XVIII. Jhrg., 1895, No. 5. 22x29 cm . 
Repr. Pp. 12. 

Chree, C. Observations on Atmospheric Electricity at the Kew Observatory 
Proc. R. S.. Vol. LX, No. 360, pp. 96-132, 1896. 

Elster, J., und Geitel, H. Bericht iiber die Ergebnisse neuerer Forschungen auf 
dem Gebiete der atraospharischen Elektricitat. 8. Jahresber. d. Vereins fiir 
Naturw. in Braunschweig. 13.5 x 22 cm . Repr. Pp. 17. [The original of paper 
presented at the International Meteorological Congress, Chicago, 1893. Cf. p. 

"Not as yet otherwise noticed in the Journal. As the conventional sizes of 
publications vary so considerably, it has been decided to give the actual outside dimen- 
sions, viz., the breadth and length, the former being given first. 



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204 PUBLIC A TIONS [Vol. I. No. 4 J 

102. The authors have called attention, in the Meteorologische Zeitschrift for 
Feb. 1896, to various errors contained in the translation ; the original should there- 
fore be consulted.] 

Eschenhagen, M. Werthe der erdmagnetischen Elemente zu Potsdam fiir das Jahr 
1895. Repr. Annalen d. Phys. und Chemie. Neue Folge. Bd. 58, 1896. 14. 5 
x 22 em . Pp. 775-776. 

. Uber die Aufzeichnung sehr kleiner Variationen des Erdmagnetismus. 

Sitzb. d. Kgl. Preuss. Akad. d. Wiss. zu Berlin. XXXIX, 18 x 25.5^. 965- 
966, 1896. 

Fleming, J. A. Electric and magnetic research at low temperatures. Lecture before 
Royal Inst, of Great Britain, June 5, 1896. Repr. I4x2i.5 cm . Pp.30. 

. The Earth a Great Magnet. Lecture delivered during the recent meeting 

of the British Association. 

Keller, F. Sull' Intensita Onzzontale del Magnetismo Terrestre nei Pressi di Roma. 
Frammenti concernenti la Geofisica dei Pressi di Roma. N. 4. Roma, 1896. 
19x270". p p j j 

Klossowsky, A. Annales de PObservatoire Me*te*orologique et Magndtique de 
rUniversite* Imperial a Odessa, pour 1895. Odessa, 1896. 24x3i.5 cm . 

Lagrange, C. Magnltisme terrestre. La de*clinaison d'une boussole libre et a 
l'e*tat statique, est-elle indlpendante de son moment magnltique ? Observations 
de de*clinometres a moments diffe*rents. Mem. d. l'Acad. roy. des sciences, etc. de 
Belgique. T. LIII. Bruxelles, 1896. 23.5 x 29 cm . Pp. 40. 2 plates. 

Marsh, C. C. Magnetic observations at the United States Naval Observatory in 1894, 
by Lieut. C. C. Marsh, U. S. N., Capt. F. V. McNair, U. S. N., Superintendent. 
Washington Observations, 1894. App. I. Washington, 1895. 23x29°". Pp. 
114, frontispiece, 12 plates. 

Paulsen, A. Re*gime magne*tique de Pile de Bornholm. Extrait du Bull.de l'Acad. 
Roy. d. Sciences et d. Lett, de Danemark, Copenhague, pour 1896. 14.5 x 23 cm . 
Pp. 42. 

Rucker, A. W., and Thorpe, T. E. A magnetic survey of the British Isles for the 
epoch January 1, 1891. Phil. Trans, of the R. S. (A). Vol. 188, London, 1896. 
24 x SO^ " 1 . Pp. 661. 14 plates. [Probably the finest testimonial to the impor- 
tance of the study of terrestrial magnetism thus far published.] 

U. S. Coast and Geodetic Survey, W. W. Duffield, Superintendent. Distribution of 
the magnetic declination in Alaska and adjacent waters for the year 1895, witn 
two charts. By C. A. Schott. Report for 1894. App. 4. Washington, 1895. 
23.5 x 29 cm . Pp. 89-100, two charts. 

. . . Notes on some instruments recently made in the Coast 

and Geodetic Survey office. By Edwin Smith. 23.5x29"". Report for 1894. 
App. 8. Washington, 1895. P P- 265-276. 4 plates. [PI. III. gives an illus- 
tration of the new C. & G. S. magnetometer and altazimuth instrument. A 
description and a reproduction of plate will be given elsewhere.] 

Weather Bureau, U. S. Department of Agriculture. Responses to Programme of 
Questions proposed for discussion at the International Meteorological Conference 
held in Paris, 1896. Prepared under the direction of W. L. Moore, chief. W. 
B. No. 104. Washington, 1896. 14.5 x 23 cm . Pp. 30. 

Wild, H. Theodolith fiir magnetische Landesaufnahmen. Repr. Vierteljahrschrift 
d. Naturf. Gesell. in Zurich, Jhrg. XLI, 1896. Jubelband. 15 x 23 cm . Pp. 26. 

. Verbesserte Constructionen Magnetischer Unifilar-Theodolithe. Mdmoires 

de l'Acad. Imp. d. Sciences de St. Pdtersbourg, VIlI. de serie. Classe Phvs.-math. 
Vol. III. No. 7. 1896. 25 x 33 cm . Pp. 32. 5 plates. 



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Terrestrial Magnetism 



An International Quarterly Journal 



Edited 6y 

L. A. BAUER 

With the Cooperation of Eminent Magneticians 



'Magnus magnes ipse est globus terrestris" 

— Gilbert, "De Magnete," 1600. 



VOLUME II 

MARCH-DECEMBER, 1897 



The Editor 

CINCINNATI, OHIO 

The University of Cincinnati 



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THE NEW YORK 

"mm? 



ASTOR.LCNOX /ND 
TILDEN FOUNDATIONS. 

R 19*0. L 



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CONTRIBUTORS TO VOLUME II 



J. Reginald Ashworth Manchester, England 

Carl Barus Providence, Rhode Island 

W. van BemmelEN Utrecht, Holland 

L. A. Bauer Cincinnati, Ohio 

Joao C. de Brito Capbllo Lisbon, Portugal 

V. Carlheim-Gyllenskold Stockholm, Sweden 

Ciro Chistoni, Modena, Italy. 

Charles Chree London, England 

Commander C. H. Davis Washington, District of Columbia 

Max Eschenhagen Potsdam, Germany 

Oliver L. Fassig Baltimore, Maryland 

J. A. Fleming London, England 

H. GEITEL Wolfenbiittel, Germany 

John F. Hayford Ithaca, New York 

Gustav Hellmann Berlin, Germany 

George W. Littlbhales Washington, District of Columbia 

Alexander McAdie San Francisco, California 

N. A. F. Moos Bombay, India 

Francis E. Nipher ... St. Louis, Missouri 

George R. Putnam Washington, District of Columbia 

Van Rijckevorsel Rotterdam, Holland 

Adolf Schmidt Gotha, Germany 

Charles A. Schott Washington, District of Columbia 

Arthur Schu^er Manchester, England 

Paul Wernicke Lexington, Kentucky 

Heinrich Wild Zurich, Switzerland 

v 



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TABLE OF CONTENTS 



GENERAL 

PAGE 

Account of a Comparison of Magnetic Instruments at Kew 

Observatory Charles Chree 133 

A Remarkable Law L. A. Bauer 70 

Electric Car Disturbances at the Magnetic Observatory of 

the United States Naval Observatory. . . . C. H. Davis 125 

Elster and Geitel's Resume of Recent Papers on Atmospheric 

Electricity A. McAdie 128 

Magnetic Work at the Kew Observatory .... Charles Chree 23 

On Methods of Making Magnets Independent of Changes of 
Temperature; and Some Experiments upon Abnormal 
or Negative Temperature Coefficients in Magnets 

/. Reginald Ashworth. 137 

On Minute, Rapid, Periodic Changes of the Earth's Magnet- 
ism M. Eschenhagen 105 

On the Distribution of Magnetic Observatories over the 

Globe Adolf Schmidt 27 

Results of Magnetic Observations on the Greenland Expe- 
dition of 1896 G. R. Putnam 32 

Secular Variation Expressions of the Magnetic Inclination 

G W. Littlehales 68 

Secular Variation in Position of Agonic Curve of North 

America C. A. Schott 123 

The Earth, a Great Magnet /. A. Fleming 45 

The Effect of Hardness on the Electrical and Magnetic 
Constants of Steel, with Particular Reference to the 
Tempering of the Magnetic Parts of Instruments 

Carl Barus 1 

The Electrification of the Atmosphere A. McAdie 61 

The Magnetic Condition of the Earth Expressed as a Func- 
tion of the Time by V. Carlheim-Gyllenskold 

Adolf Schmidt 150 
•ical Curves of Secular Variation of Magnetic Declination 

in Northern Hemisphere L. A. Bauer 124 

3ER die Fehler bei Erdmagnetischen Messungen . . H. Wild 85 

*tical Earth- Air Electric Currents L. A. Bauer 11 

vi 



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TABLE OF CONTENTS v ii 



LETTERS TO EDITOR 



PAGE 



A Proposal with Regard to an International Magnetic Congress 

A. Schuster 35 

Results of the Magnetic Observations on the Rigi in 1895 and '96 

Van Rijckevorsely van Bemmelen 76 

Results of Magnetic Observations at the Observatory Infant D. Luiz 

(Lisbon), 1890-96 /. Capello 119 

Sur rinclinaison de P Aiguille Aimantee a l'Epoque Etrusque 

V. Carlheim Gyllenskold 117 

S. Stevin's AIMENETPETIKH G. Helhnann 72 

The Assam Earthquake of June, 12, 1897 — A Request for Data 

„ R. D. Oldham 156 

The Latitude Variation and the Earth's Magnetism . J.F. Hay ford 156 
" The Non-Cyclic Effect " und " Die Erdmagnetische Nachstorung " 

W. van Bemmelen 74 

" The Non-Cyclic Effect " und " Die Erdmagnetische Nachstorung " 

C. Chree 115 

NOTES 

Corrigenda 44 

Editorial Notice 43 

Magnetische Landesaufnahtue der Norddeutchen Gebiete 44 

Obituary 157 

The Elementary Pulsations of the Earth's Magnetism 84 

The Magnetic Survey of Maryland 76 

The Magnetic " Variation " and Dip for the Year 1897 157 

The Mean Values of the Magnetic Declination for Parallels of Lati- 
tude . 157 

ABSTRACTS AND REVIEWS 

PAGE 

Baker, M. : The Boundary Monuments of the District of Columbia 160 

Baschin, O.: Bibliotheca Geographica O^L. Fassig 159 

Cari,heim-Gyu,ensk6ld, V. : Determination des Elements Magnet- ^ 

iques dans la Suede Meridionale pendant Pannee, 1892 

G. W. Littlehales 81 

Chree, C. : Non-cyclic Effects at Kew Observatory during the Selected 

" Quiet " Days of the Six Years, 1890-95 . . W. van Bemmelen 77 

Coast and Geodetic Survey : The New Coast and Geodetic Survey 

Magnetometers 38 

Folgheraiter, G. : Richerche sulK inclinazione magnetica all, epoca 

etrusca C. Chistoni 78 

Hann, J. : Die Erde als Ganzes, ihre Atmosphare und Hydrosphare 

0. L. Fassig. 159 

Hellmann, G. : Neudrucke von Schriften und Karten iiber Meteor- 

ologie und Erdmagnetismus, No. 9, Henry Gellibrand's. "A 

Discourse Mathematical on the Variation of the Magnetical 

Needle " L. A. Bauer 83 



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viii TABLE OF CONTEXTS 

PAGE 

Lagrange, C: Is the Declination Independent of the Magnetic 

Movement of the Needle? . F. E. Mipher 37 

McAdie, A. : Equipment and Work of an Aero-Physical Observatory 

H. Geitel 82 

Preston, E. D. : Magnetic Observations at High Altitudes 41 

Schott, C. A. : Secular Variation of the Earth's Magnetic Force in 

the United States and in Some Foreign Countries 39 

Van Rijckevorsel and van Bemmelen : Observations magn&iques 

en Suisse, executees in 1895 P. W. 38 

t 

PUBLICATIONS 

' List of Published Papers on Terrestrial Magnetism by the late 

Charles Chambers /&. A. F. Moos and Z,. A. Bauer 1 20 

List of Recent Publications 83 

List of Recent Publications 162 



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Volume II Nu&ber i 

Terrestrial Magnetism, Marchfi8ffi K 



THE EFFECT OF HARDNESS ON THE ELECTRICAL AND 
MAGNETIC CONSTANTS OF STEEL, WITH PARTICU- 
LAR REFERENCE TO THE TEMPERING OF THE MAG- 
NETIC PARTS OF INSTRUMENTS. 

By Carl, Barus. 

At the request of the Editor, I subjoin certain results in the tem- 
pering of magnetic needles, as obtained by Dr. Strouhal and myself 1 
some years ago. A full account of the work will be found in the 
Bulletin of the U. S. Geological Survey, No. 14, 1885, from which 
the following notes are taken. 

The remarks in this memoir refer almost exclusively to the spe- 
cies of hardness known as temper, and which may be imparted to 
iron-carburets by sudden cooling from red heat combined with 
more or less subsequent annealing. 

If we define the structure of a hard cylindrical steel rod as be- 
ing the law of variation of density encountered on a passage from 
axis to circumference along any radius of the rod, then structural 
identity in case of two given geometrically similar rods of the same 
composition a priori implies identity of diameter. In what way 
structure may vary with diameter is not even conjecturable. It fol- 
lows that immediately comparable magnetic data are to be antici- 
pated only where the rods of variable hardness and length retain 
the same thickness and composition throughout the course of the 
experiments. 

1 Barus: Phil. Mag. (5), viii, p. 341-368, 1879. 

Strouhal and Barus: "Anlassen des Stahls und Messung seines Hartezu- 
standes." Wied. Ann. xi, pp. 930-997, 1880. 

: Anderung der thermoelectrischen Stellung des Eisens und des 

Stahls durch Magnetisirung. Wied Ann., xiv, pp. 54-61, 1881. 

: Uber den galvanometrischen Temperatur — Coefficienten des 

Stahls. Wied. Ann., xx, pp. 525-536, 1883. 

Einfluss der Harte des Stahls auf dessen Magnetisirbarkeit. Wied. Ann., xx, pp. 
621-^62, 1883. 

, Einfluss des Anlassens auf die Haltbarkeit der Magnete. Wied. 

Ann., xx, pp. 662-684, 1883. 

Recent papers refer more particularly to the relation of hardness and viscosity. 

1 



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2 CARL BARUS [Voc n, No. i.) 

If the temperature from which steel is suddenly cooled be sup- 
posed to increase continuously from a very low value to the highest 
admissible, the hardness of the chilled rod will remain compara- 
tively inappreciable until a certain critical temperature in red heat 
is reached. At this stage, and a little beyond, hardness increases at 
exceedingly rapid rates with temperature, after which the rate again 
decreases. 

Having observed, at the outset of these researches (in 1878), that 
both the specific electrical resistance and the thermoelectric power 
of steel varies at a phenomenally rapid rate with its state of temper 
between hard and soft, it seemed expedient to express the hardness 
of the metal in terms of these variables. So understood, the hard- 
ness of steel, in any state of temper, may be defined with an accu- 
racy of 1 in 1,000. An advantage was thus secured over the older 
methods, in which hardness is rated in terms of the oxide films, or 
by other equally vague methods. 

The largest observed variation of thermoelectric power pro- 
duced by tempering is 12.8 microvolts per degree centigrade at o°. 
The largest ratio of the respective resistances of hard and soft steel : 

45 (cm /cm*, o° microhm) : 15 (cm /cm 8 , o°, microhm) =3. 

In recent experiments these ratios have even been exceeded. 

Since hard and soft steel lie on opposite sides of pure silver in 
the thermoelectric scale, maxima and neutral points of electro- 
motive force (thermoelectric inversions) are a common occurrence. 

The annealing effect of any temperature acting on glass-hard 
steel increases gradually at a rate diminishing continuously through 
infinite time — diminishing very slowly in case of low temperatures 
(<ioo°), very rapidly at first, then again slowly in the case of high 
temperatures (>2oo°); so that the highest and hardest of the infe- 
rior states of hardness possible at any given temperature is 
approached asymptotically. 

These results are graphically given in the appended Figure 1, 
the ordinates being thermoelectric powers relatively to silver and 
the abscissae, hours of exposure to the action of the annealing bath. 
The temperature of this bath is added at the end of each curve. 
Inasmuch as the thermoelectric power of hard steel is very near 
that of silver, whereas soft steel is remote from it, the ordinates 
here form a scale of decreasing hardness. Thus the abscissa is 
practically a glass-hard steel rod. The figure contains mean values 
of a great number of results. Clearly the degree of hardness 
retained by a glass-hard rod, after having been subjected to the 



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THE TEMPERING OF MAGNETS 3 

operation of annealing, is dependent both on the temperature to 
which it has been exposed and on the interval of time during which 
this exposure has taken place, in such a way that the effect of time, 
though of predominating importance in the case of small values of 
temperature, is more and more negligible in proportion as these 
values increase. 



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Figure 1. — Hard wires annealed continu- 
ously at o°,66°, ioo°, 185 , 330°, and 1000 , 
respectively. 

The ultimate annealing effect of any temperature t° is independ- 
ent of the possibly pre-existing effects of a temperature /'°, and is 
not in any way influenced by subsequent applications of the latter, 
provided />/. In case of partial annealing at t° (time finite) this 
law applies more fully the more nearly the said ultimate effect of t° 
is reached. 

If hardness of steel is to be expressed therm oelectrically, it is 
inexpedient to use the soft state as a point of departure. The 
thermoelectric difference between soft steel and soft iron (say 1) 
when compared with the corresponding difference between the ex- 
treme states of steel (say 10) is small. In soft steel, however, the 
effect of foreign ingredients (impurities: S, P, Si, etc.) is still tco 
pronounced to admit of a desirably accurate determination of the 
thermoelectric position of this metal. 

In the case of steel, the relation between thermoelectromotive 
force per degree centigrade at o°, and specific resistance at o° (s), 
is linear throughout the whole of the phenomenal range of variation 
of these qualities with hardness. This law suggests the introduc- 



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CARL BARUS 



[VOL. II, No. I.J 



tion of the new variable thermoelectric hardness ih), defined thus: 
Suppose the said law of linear variation to be true indefinitely; 
then will the electromotive force microvolt » per degree centigrade 
at o° of a thermo-element consisting of steel in the imaginary nor- 
mal state whose specific resistance -cm cm s o° microhm) is zero, 
and steel in any given state, be the thermoelectric hardness of the 
latter. The thermoelectric position of steel in the stated normal 
condition, with reference to pure soft silver, is 

m -15.18 microvolts 
per degree C. at o°. Finally in the fundamental equation h=n s, 

n=o.4i2. 
Like the specific resistance, the galvanic temperature-coefficient 
of the iron-carburets exhibits a phenomenal range of variation, 
passing from the values for wrought iron and soft steel, 0.0052 and 
0.0043, respectively, to the values for hard steel and cast iron, 0.0016 
and 0.0013, respectively. The said coefficient decreases continu- 
ously and uniformly as resistance increases, more rapidly than the 
latter during the earlier stages, much more slowly during the later 
stages of a progress from iron to cast iron. An inferior limit of the 
temperature-coefficient would therefore seem to appear much before 
the iron-carburet reaches the superior limit of resistance. If classi- 
fied with reference to the relation between resistance and tempera- 
ture, the iron -carburets as a whole form one continuous series. 
Figure 2 exhibits the relation between specific electrical resistance 
(abscissa) and temperature coefficient (ordinate) for wrought iron, 
for steel, and for cast iron. 





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Figure 2. — Relation between specific elec- 
trical resistance and temperature-coefficient 
for wrought iron, for steel, and for cast iron. 



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THE TEMPERING OF MAGNETS 5 

If a be the temperature-coefficient and r , the specific electrical 
resistance of steel at o° C, then r Q (a -j- m)-~n, to a high degree 
of approximation ; m and ;/ are constants, which if r Q is given in ab- 
solute units (microhm cm s ), have the values: 

tn -- — 0.000303 ± 0.000079, n = + 0.0620 ± 0.0017. 

This law may even be extended so as to include soft iron on the 
one hand and cast iron on the other. Its general bearing is dis- 
cussed elsewhere. 1 

Both the galvanic and the thermo-electric effects of magnetiza- 
tion are negligible in comparison with the corresponding electrical 
effects of tempering — the former amounting to less than 0.3 per 
cent of the latter in the most unfavorable case. 

The absolute value of the said thermoelectric effect for magnet- 
ically saturated iron is + 0.035 microvolts per degree centigrade, at 
zero. 

The thermoelectric effects of a temporary tensile strain in iron 
and of magnetization are qualitatively alike. Hence we might infer 
that the latter effect is to be attributed to the strain which accom- 
panies magnetism. 

Rigidly comparable data of the relation between magnetism and 
hardness are not readily obtainable except with magnets which 
were originally integrant parts of the same (hard) steel rod of uni- 
form temper throughout its length. The plan of experimentation 
is expediently made to conform with a passage from hard to soft. 

If magnetic moment (C. G. S.) per unit of mass (g) be regarded 
as a function of hardness, the family of curves obtained exhibits 
the following general character : Magnets, whether long or short, 
after incipient annealing from the glass-hard state diminish in mag- 
netizability to a pronounced minimum of this quality. If the 
annealing be continued, magnetizability again increases to an 
enormously developed maximum in case of rods of large dimension- 
ratio, to a flat or indistinct maximum in case of small dimension- 
ratio. On passing from long to short steel rods the minimum is 
found to move in a direction from hard to soft, at very slow rates, 
thus remaining in the region of glass-hardness; the maximum, on 
the other hand, in a direction fro.u soft to hard, at somewhat more 
rapid rates. The unique maximum of permanent magnetizability 
will probably be exhibited by a linear steel rod, annealed from 
glass-hardness as far as the physical state of maximum density. 

» Barus: Am. Jour, of Science, XXXVI, p. 427, 18XS; or, Bulletin, U. S. Geol. 
Sur., No. 54, Chap, iii, 1889. 



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CARL BARUS 



[Vol. ii, No. i] 



The value of the unique maximum is demonstrably much above 
785 C. G. S. units of intensity, or 100 C. G. S. units of moment per 
gramme-mass. Continued diminution of the dimension- ratio, finally, 
will probably bring the said minima and maxima into coincidence 
in such a way that permanent magnetizability decreases uniformly 
from hard to soit. 

These points are fully borne out by the annexed graphic repre- 
sentation (Fig. 3), showing the relation between specific magnet- 
ism and hardness of steel for different dimension- ratios. 




Wire* it **talftrlhm 
O OSlt 




Figure 3.— Relation between specific magnetism and hardness 
of steel for different dimension ratios. 

In the diagram the ordinates denote magnetic moments per unit 
of mass. The corresponding values of magnetic intensity were, 
therefore, to be found by multiplying by 7.65, the mean density of 
the steel. The abscissas are degrees of hardness expressed in terms 
of the specific resistance (cm 3 microhm) of the steeL The numbers 
a attached to the curve are the dimension-ratios, length /diameter. 



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THE TEMPERING OF MAGNETS ? 

The family of magnetic curves must be separately investigated 
for each given diameter (structure) and each given degree of car- 
buration. If magnetic moment per unit of mass be regarded as a 
function of the dimension-ratio (a = length, /diameter), the family 
of curves obtained (conveniently described with the aid of the four 
type curves: "glass-hard," "yellow annealed," "blue annealed," 
" soft,") exhibit the general character described below. (See Figure 
4, exhibiting relation between specific magnetism and dimension- 
ratio of steel rods, for different degrees of hardness.) 

The diagram contains a comparison of four typical degrees of 
hardness, expressed in terms of the color of the oxide film, so that 
"soft," " blue annealed," "yellow annealed," "glass-hard" make a 
scale of increasing hardness. The specific resistances (cm\ microhm) 
would be 15.9, 20.5, 26.3, 45.7, respectively. The ordinates are the 
values of magnetic moment per unit of mass (volume 1 / 7.65 cm s ), 
and the abscissae, the corresponding ratios of length to diameter. 





























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Figure 4. — Relation between specific magnetism and dimension- 
ratio of steel rods, for different degrees of hardness. 

The curve " glass-hard " is concave as regards the axis of ab- 
scissae (dimension-ratio) throughout. Rising very rapidly at first, 
it finally ascends to a distinct limiting value or horizontal asymp- 
tote. The curve " soft," on the other hand, rises very slowly in its 
earlier stages, and is convex as regards the axis of abscissae. From 
here it passes rapidly through a point of double inflection into con- 
cavity, and then above the former curve. Finally, the rate of as- 
cent again decreases, so that a horizontal asymptote is also reached, 
but apparently at a later stage of progress than is the case with 
hard steel. 



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8 CARL BARUS Ivol ii, no. i] 

From either of these two loci, expressing the variations of the 
extreme states, we may, by annealing, pass continuously to the 
other. But the manner of such passage, from the one curve to the 
other, in consequence of the continuous change of parameter (hard- 
ness), is exceedingly complicated. Incipient annealing of glass-hard 
steel produces a distinct, though relatively small, descent of the 
original curve as a whole. As annealing progresses, the farther 
end of the curve is always the first to rise and to pass above the 
original curve in such a way that the point of intersection of the 
new curve and the original curve (glass-hard) moves along the 
latter with great rapidity, from greater to smaller values of the 
dimension-ratio. When the curve "yellow annealed " is reached, 
the part of it between a small value of the dimension-ratio, a (— 14 
and 18, in the above measurements, for diameters 2 p = 0.08 cm and 
0.15 cm), and a — 00, has been already elevated above the curve 
" glass-hard. " At the stage of progress given by the blue annealed 
curve, the part between another small value of « (« — 15 and 20 in 
the above results), and a = 00 has risen far more rapidly than before,, 
while, on the other hand, the advancing part of curve between a=_o 
and the said small value (« ~ 1 5 or 20, respectively) having de- 
scended very gradually, is now distinctly convex downward. Pass- 
ing from "blue annealed" to "soft," the part of the curve above 
smaller dimension-ratios continues to fall, in general at greater 
rates, finally to merge into the curve "soft." The remaining part, 
above greater dimension-ratios, still rises slowly, reaching its supe- 
rior elevation, from which it then also falls rapidly into coincidence 
with the extreme curve "soft." During this last phase of progress 
the point of intersection of the advancing curve and the curve 
glass-hard passes along the latter from smaller to larger values of 
the dimension-ratios. 

In considering the permanent magnetic effect of temperature on 
steel permanently saturated, it is necessary to discriminate sharply 
between two species of magnetic loss : 

1. The direct effect, due simply to the action of temperature, 
and to be ascribed to diminution of coercive force and to interfer- 
ence of thermal expansion with the magnetic strain. 

2. The indirect effect, due to the action of temperature in pro- 
ducing mechanical annealing, and to be ascribed to the interference 
of the rearrangement of molecules resulting, with the magnetic 
strain. 

The two effects are frequently superimposed. Considered sep- 



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THE TEMPERING OF MAGNETS 9 

arately, the latter (indirect effect) is by far the greater in amount, 
and its character, with regard to magnitude and duration, fully typi- 
fied by the concomitant phenomenon of ordinary mechanical 
annealing. The former (direct effect) is not only of smaller mag- 
nitude, but subsides completely within a very much smaller interval 
of time. A third (temporary) effect of temperature does not fall 
within the scope of the present work. If the contemporaneous 
effects of the action of temperature on permanently saturated glass- 
hard magnets — viz., reduction of magnetic moment per unit of mass 
(ordiuates) and of specific resistance (abscissae) — be compared graph- 
ically, the loci of the relation pass from pronounced convexity, as 
as regards the axis of abscissae, almost horizontally through a point 
of circumflexion into pronounced concavity. It must be borne in 
mind that both the direct and indirect effects are here superimposed. 
The said curves, if constructed for different dimension-ratios, are 
approximately parallel, presenting greater curvature, however, for 
smaller dimension-ratios than for larger. The immediate bearing 
of temper on the indirect effect is strikingly shown by the fact that, 
in the case of long, hard, permanently saturated steel rods, the rela- 
tion between permanent magnetism per unit of mass and resist- 
ance, where both variations are simultaneous and due to changes 
of temper only, and where the latter occurs between the maximum 
of permanent hardness for ordinary temperature and the maximum 
of the same quality for ioo°, is ultimately (a=oc) linear. 

The maximum of permanent magnetization for any given tem- 
perature, /°, which can be imparted to a steel rod exhibiting the 
maximum of permanent hardness for the same temperature, /°, is 
wholly independent of the possibly pre-existing states of magneti- 
zation. If / = ioo°, such magnets possess exceptional stability, 
both as regards effects of (atmospheric) temperature and time and 
of percussion. 



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IO CARL BARUS [Vol. II, No. i.) 

The following rules for the practical treatment of magnets, 
where great secular permanence of magnetization is the principal 
desideratum, are submitted : 

/. Rods tempered glass-hard are not to be used as essential parts 
of magnetic instruments. 

2. Having tempered a given steel rod in such a way as insures 
uniformity of glass- hardness throughout its length, expose it for a 
long time {say 20-30 hours; in case of massive magnets even longer 
intervals of exposure are preferable) to the annealing effect of steam 
(ioo°). The operation may be interrupted as often as desirable. The 
magnet will then exhibit the maximum of permanent hardness for ioo°. 

3. Magnetize the rod — whether originally a magnet or not is quite 
immaterial — to saturation, and then expose it again for about 5 hours 
(in case of massive magnets even larger intervals of exposure are 
preferable) to the annealing effect of steam (ioo°). The operation 
may be interrupted as often as desirable. The magnet will then ex- 
hibit both the maximum of permanent magnetization as well as the maxi- 
mum of permanent hardness corresponding to ioo°. Its degree of mag- 
netic permanence against effects of temperature (Ooo°), time, and 
percussion is probably the highest conveniently attainable. 1 

1 The remaining subjects of the Bulletin cited will not specially interest magne- 
ticians. They adduce a physical diagram for the classification of iron carbides 
(wrought iron, steel, cast iron). In subsequent Bulletins of the U. S. Geological 
Survey (Cf. Bulletins, No. 27, pp. 30-62, 1886; No. 35, pp. io-6i, 1886; No. 73, pp. 
i-i35i I 89 I ; No. 94, pp. 17-135, 1892) other physical properties of steel are discussed 
in part, with particular reference to their bearing on the theory of solid viscosity. All 
of the Bulletins may be obtained at merely nominal prices by addressing the Director 
of the United States Geological Survey. The Bulletin (No. 14), cited in the begin- 
ning of this paper, consists of 240 pages, and costs fifteen cents. 

Brown University, Providence, R. I. 



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VERTICAL EARTH-AIR ELECTRIC CURRENTS. 1 
By L. A. Bauer. 

It is well known that the earths " permanent " magnetic field is a 
most complex one. Gauss was the first to show how to analyze 
this field mathematically without making any assumption with 
regard to the actual distribution of the magnetism within the earth's 
crust. For a first attempt, he found it sufficient to embrace in his 
analytical expression terms to the fourth order. With the excep- 
tion of the first-order terms, which represent a homogeneous mag- 
netization about a diameter 1 inclined to the earth's rotation axis by 
an angular amount of about 12 , no physical interpretation of the 
various terms has as yet been given. As the eye is often quicker 
than the mind to perceive the relationship of apparently dissimilar 
things, I am attempting to give graphical representations of the 
various terms or components involved. In a paper presented be- 
fore the last meeting of the American Association for the Advance- 
ment of Science, 8 I represented, graphically, the field that remains 
after deducting that part which can be referred to a homogeneous 
magnetization, as stated above. At once the eye correlated phe- 
nomena which, apparently, had no connection with each other, but 
which now, seemingly, possessed similar characteristics. I have 
satisfied myself that it will be possible to resolve this residual field 
still further into components physically interpretable. As we suc- 
ceed in evaluating these components, they will be subtracted suc- 
cessively from the residual fields until we finally obtain that part 
which must be referred purely to the heteorogeneous structure of 
the earth, and which, in consequence, cannot be further resolved. 

Among other things, the residual field, referred to above, exhib- 
ited a relationship with such phenomena as could be referred to 
electric currents passing from the earth into the air, and from the 
air into the earth. If there are such currents that are continuous, 
they, of course, have made themselves felt in the formation of the 

1 Presented before the Philosophical Society of Washington, January 9, 1897. 
* This diameter is very nearly parallel to the chord joining the so-called "mag- 
netic poles of the earth." 

8 Abstract published in this Journal, Vol. I, No. 4. 

n 



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12 



L. A. BAUER [vol. n, No. i.] 



permanent magnetic field and form part of the residual field. One 
of the first steps, then, must be to eliminate the effects of these 
currents, if they are appreciable. An inquiry with regard to the 
existence of vertical earth-air electric currents 1 forms, therefore, the 
subject of the present paper. 

If such currents exist, their presence will be indicated by the 
non-vanishing of the line integral of the earth's magnetic force 
revolved along a closed curve of the earth's surface. If the line 
integral vanishes, then all of the earth's magnetic force is to be 
referred to a potential, and there are no currents which pass from 
the air into the earth or back again. 

Gauss carried out this test in a special case, and found the in- 
tegral to be practically zero. He therefore proceeded on the 
assumption that the entire force was due to a potential, and found 
that, as far as the material at his command would permit him to judge, 
the expression developed on this hypothesis represented the earth's 
magnetic state probably within the errors of observation. Since 
his time, the earth's magnetic potential has been re-computed, with 
the aid of more complete data, by Erman-Petersen, Icilius, Neu- 
may er- Petersen, and lastly, by Adolf Schmidt, of Gotha. The 
Neumayer-Petersen computation showed conclusively that if the 
Gaussian analysis be extended to include terms of the fifth order, 
it fails to embrace the entire observed field. The differences between 
observation and computation were of such an extent and nature as 
to preclude their being accounted for wholly by errors of obser- 
vation. 

Schmidt, hence, discarded the potential hypothesis; i. e., did not 
assume ad initio the existence of a function to which all the com- 
ponents of the force (northerly, easterly, and nadir) could be 
referred He, consequently, in his most painstaking analysis, made 
a separate adjustment of each of the three components, and obtained 
three analytical expressions, instead of Gauss's single expression. 
By comparing these expressions with each other, according to prin- 
ciples that can not be developed here, he was enabled to draw the 
following conclusions :* 

The earth's magnetic force consists of three parts, viz.: i. The 
greatest part — this is to be referred to causes within the earth's 

1 This name has been given such currents by Professor Riicker. Cf.> Vol. I, No. 2. 

* Mitteilungen uber eine neue Berechnung des erdmagnetischen Potentials. 
Von A. Schmidt, in Gotha. Abh. d. II. CI. d. k. bayer. Ak. d. Wiss. XIX. Bd. I 
Abth. p. 32, Mtinchen, 1895. 



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VERTICAL EARTH-AIR ELECTRIC CURRENTS 13 

crust, and possesses a potential. 2. The smallest part, about ?V of 
the entire force — this is due to causes outside the earth's crust, and 
likewise possesses a potential. 3. A somewhat larger part than the 
preceding — this does not possess a potential, and, in consequence, 
points to the existence of vertical earth-air electric currents. These 
currents amount, on the average, for the entire earth's surface, to 
one-sixth of an ampere per sq. km. 

When Neumayer made known the results of his computation, it 
occurred to the writer to make more elaborate tests of the vanish- 
ing of the line integral of the force than Gauss had done; viz., to 
carry out this integral for latitudinal circuits of the earth. During 
the past two years the writer has had occasion to refer to the results 
of his researches at various times. A brief summary was submitted 
to the Committee on Grants of the American Association for the 
Advancement of Science at the Buffalo meeting. The results he 
had obtained thus far all seemed to confirm Schmidt's conclusion 
as to the existence of currents. 

Professor Riicker, on the other hand, could find "no evidence in 
favor of the existence of vertical currents" over a region of the 
earth— the British Isles — which had been very minutely surveyed. 1 
He, of course, did not wish to be understood as concluding that 
therefore there are no such currents in other parts of the earth. 

A few days ago I received from Dr. Schmidt, in manuscript, the 
northerly, easterly, and nadir (vertical) components for all points at 
distances of five degrees in latitude and longitude, between 6o° 
north and 6o° south. I have thus had the opportunity of revising 
my previous results. Only a slight modification was needed. I take 
great pleasure in embracing this opportunity to give public expres- 
sion of my indebtedness to Dr. Schmidt lor his ready and generous 
response to my request for these components. They represent 
many hours of hard work, and are based upon the values of declina- 
tion, inclination, and horizontal intensity which Neumayer scaled 
from his original magnetic maps for 1885. The figures given 
below are based on this material. 

A word with regard to the value of such material. If I wish to 
carry out the idea of taking the line integral of the force around 
the earth along a parallel of latitude, I must depend for the values 
of the force upon magnetic maps. I therefore do not make use 
of directly observed quantities. The maps are necessarily more 
or less in error. Such a method must therefore be adopted as 

1 C/.y Vol. I, No. 2. 



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14 



L. A. BAUER [vol. n, No. ij 



will eliminate, as far as possible, these map errors from the final 
results. 

The following consideration will show that this has been done: 

A magnetic map — e. g. t an isogonic chart — is, in a certain sense, a 
graphical adjustment of the material at hand. For the entire region 
embraced by the map, it follows, then, that the isomagnetic lines 
will not always be in error in the same direction. In some parts, 
the correction will be positive; in others, negative. The chart 
thus, though it may be faulty in detail, may, nevertheless, give a 
fair general, or average, representation. The Neumayer magnetic 
maps are based upon many thousand observations made under the 
most varied conditions. It was my privilege to become acquainted 
with Prof. Neumayer's painstaking methods and his unsurpassed 
material. I am convinced that he has given us the best maps to be 
had at present. Of course, there are large regions of the earth 
where, by reason of an imperfect knowledge of the secular varia- 
tion, the existing observations could not be accurately reduced to 
the epoch 1885, or again, regions where, by reason of no existing 
observations, the lines had to be more or less conjectural. From 
the foregoing remarks it will be evident, however, that if the inves- 
tigation is extended over the entire region of the map, the map 
errors, being in the nature of "accidental ones," will be eliminated 
to a greater or less extent from the average result. Again, suppose 
the line integral is taken over areas of such extent that the map 
error over them may be regarded as having the same sign. If this 
map error be likewise nearly of the same magnitude over the region, 
then the error will be almost entirely eliminated in taking the line in- 
tegral around the region. Both precautions have been taken. The 
results given are the results of integrations (summations) over areas 
of the earth's surface bounded by five degrees in latitude and longi- 
tude. Each latitudinal summation is the result of 72 partial sum- 
mations, and the final result is dependent upon 72x25= 1,800 
summations. 

This explanation was deemed necessary to make it possible to 
form some opinion as to the value of the conclusions reached in 
this paper. 

If IV be the total work done in moving a unit magnetic pole 
around a closed curve on the earth's surface, //, the horizontal com- 
ponent of the earth's magnetism, e, the angle H makes with the 
tangent to the curve, dl the curve-element, /, the intensity in 
electro-magnetic units of the closed electric currents passing from 



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VERTICAL EARTH-AIR ELECTRIC CURRENTS I5 

one side of the surface inclosed by the curve to the other side, 
then, is: 

W = C H cos c dl = 4 tz I. (i) 

If the direction in which the integral is taken be anticlockwise, 
then will a plus value indicate an upward current — i. e. } one that 
passes through the earth's surface into the air — while a negative 
integral would indicate a downward current, or an air-earth current. 

Taking a parallel of latitude as the closed circuit, and going in 
an easterly direction, H cos e is simply the easterly component, Y n 
of the earth's magnetic force, and dl the arc element of longitude. 
Suppose we knew Y, for each degree of longitude, then we could 
substitute for the integration sign the summation sign, and thus: 



W 



= ^ 2! * = * * 7 - 



In this formula we are only taking account of the vertica <com 
ponents of the electric currents. The components tangential to 
the earth's surface contribute nothing to the summation. They 
would form a part of the earth's magnetic force which can be 
referred to a potential. Whether they constitute that part of the 
potential which is due to outside causes, as revealed by Schmidt's 
analysis, and whether they are the source of the so-called " earth- 
currents," are interesting questions. The quantity, /, in (2) is the 
resultant quantity of electricity which passes in a unit of time per- 
pendicularly through the surface inclosed by the parallel of latitude ; 
i.e., through the zone between the circle of latitude and the pole. 

The resultant current passing through a zone bounded by two 
parallels <p x and <p 2 would be if ?» > ?i : 

&f=A-A=X*ldl l 2; Y.~-dl,2> Y] 

In other words, if we carry out the summation for areas founded 
by the latitudes <p t and <f u and by two meridians, and add together 
the partial summations, then the meridional summations mutually 
cancel each other, and we simply have left the latitudinal quantities. 
Consequently, in the present paper, which is concerned with the 
average distribution of vertical currents, the summation extends, 
for each parallel of latitude, over the easterly components alone. 

Since I possess these components for intervals of five degrees in 
longitude, instead of one degree, as above supposed, the right-hand 
member of (3) must be multiplied by five. Of course, the summa- 



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!5 L. A. BAUER [vol. n. No. i] 

tion of these components is only an approximation to the value of 
the integral in (i). I have satisfied myself, however, that the values 
thus obtained are sufficiently close for the purpose at hand. The 
proper way would be to obtain the integral by mechanical quadra- 
ture. Looking over the Y values, it is found that, on the average, 
the change in the Ys for a io° interval is very nearly linear. I 
have, therefore, contented myself, for the present, with the above 
method of procedure. 

Now, let i be the average current intensity per sq. cm.; then will 
/\ / = i A, A being the area in sq cm.'s of the zone. We have 
A= 2* R (sin <f ,-sin <f ,), dl =2* R cos 9 /360, R being the earth's 
mean radius. If / and i are to be expressed in amperes per sq. cm., 
we must further multiply the right member of (3) by ten. The final 
equation becomes : 

,• ,= T 5 i /? ( cos ,jr ^ Y t — cos ? ^ Y, ) 

2 r R* (sin y 2 — sin jr.) 
- /. - /. (4) 



In the table opposite, IY t is given in units of the fourth decimal 
C. G. S., /and A /, in units of 10,000 amperes, and i in thousandths 
of an ampere per sq. km. It should be recalled that, according to 
the potential hypothesis, the quantities given in the second and 
third columns ought to have been zero, if there were no cumulative 
effects due to errors of observation. It will assist the conception of 
the magnitude of the figures given in these columns to put the 
result in the following form : The average value of the component 
of the earth's total magnetism, resolved in the direction of a parallel 
of latitude, is about 0.06 C. G. S. for the entire globe ; the average 
value of that part of the latitudinal component which can be re- 
ferred td* vertical electric currents, for the region between 60 N and 
60 S, is 0.0014 G. G. S. t a quantity easily within reach of our absolute 
instruments. Hence, on the average, about ft of the latitudinal 
component of the earth's entire magnetism can be referred to an effect 
simitar to that of continuous vertical electric currents} Note that there 
is a systematic variation in the quantities with latitude, and that the 
sign is reversed in approaching the equator and when passing into 
the southern hemisphere. It would be difficult to ascribe such a 

Cy„ Schmidt's statement, page 13. 



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VERTICAL EARTH-AIR ELECTRIC CURRENTS 



17 



systematic variation and reversal of sign to errors of observation, 
or, rather, to map errors, which, as already explained, partake largely 
of the nature of " accidental errors." 





2Y. 


/ 


A/ 


i 


Latitude. 


N 


5 


N 


5 


N 


5 


N 


5 


Mean. 


60 


+ 271 


+ 992 


+ 60 


+219 






















+ 42 


+326 


+ 35 


+274 


4-154 


55 


+ 40I 


— 422 


+ I02 


— 107 






















+ 141 


+303 


+ 104 


+224 


+ 164 


SO 


+ 856 


—1445 


+243 


—410 






















+ 135 


+238 


+ 9i 


+ 159 


+ 125 


45 


+ 1313 


—3078 


+378 


—648 






















— 20 


+ 37 


— 12 


+ 23 


4- 6 


40 


+ 1057 


— 2022 


+358 


-685 






















— 32 


— 39 


— (8 


— 22 


— 20 


35 


+ 900 


-1784 


+326 


—646 






















— 66 


- 76 


— 35 


— 40 


- 38 


30 


+ 680 


-1489 


+260 


—570 






















—118 


—151 


— 60 


— 77 


— 68 


25 


+ 3& 1 


— 1048 


+ 142 


—419 






















—132 


—175 


-64 


-85 


— 74 


20 


+ 23 


-587 


+ IO 


—244 






















—166 


-64 


— 79 


— 30 


— 54 


15 


-366 


— 422 


-156 


—180 






















—155 


+ 58 


— 72 


+ 27 


— 22 


10 


— 714 


— 547 


—3" 


-238 






















-185 


+ 97 


-84 


•+ 44 


— 20 


5 


—1 128 


— 762 


—496 


—335 






















+ 79 


+ 82 


+ 36 


+ 37 


4- 36 


Equator. 


— 944 


— 944 


—417 


—417 













The meaning of the figures in the other columns will be clear 
from an example. Over the surface between the north pole and 
latitude 45 N> the upward currents exceed the downward by 3,780,- 
000 amperes, while, if we extend the surface considered, down to 
latitude 45 ° S, the downward currents exceed the upward by 6,480,- 
000 amperes. To express the latter result in another way : Be- 
tween 45 N and 45 ° 5, the current is, on the average, directed 
downward ; i. e. t passes from the air into the earth. For the zone 
between 45 ° A^and 50 N y we have a resultant upward current of 
1,350,000 amperes, or, on the average, 0.091 ampere per sq. km. 
This does not mean that for every sq. km. in that zone there is an 
upward current of that strength. In fact, as other investigations 
which I am conducting have shown, over part of that zone the cur- 
rent may be upward; over another part, downward; and over still 

3 



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i8 



L. A. BAUER 



[Vol.. II, No. i.) 



another, vanish entirely. 1 The result given if an average quan- 
tity and has simply a statistical significance. 

In the annexed figure, I have shown, graphically, the distribu- 
tion of the average vertical currents for a geographical meridian — 
i. e. y the radial ordinates represent the quantities, i; the direction of 
the average current is indicated by the arrow. 




It would appear as though there might, possibly, be some con- 
nection between upward electric currents and the lows of the gen- 
eral atmospheric circulation and between downward electric currents 
and atmospheric highs, but this matter requires further investigation. 

1 Riicker's results may find an explanation in this way ; viz. % that the British 
Isles lie in a belt where the upward and downward currents practically neutralize 
each other. 



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VERTICAL EARTH-AIR ELECTRIC CURRENTS 19 

With respect to these currents, we can divide the earth into four 
zones, over which the sum of the upward currents is equal to that 
of the downward ones. Thus: 

Zone. Approximate Boundaries. 

I. North Pole — 65 (?) N. 

II. 65 (?) N — 20 N. 

III. 20 N — 57 S. 

IV. 57 S — South Pole. 

The distribution of the currents is, therefore, not symmetrical 
about the geographical equator. 

In their general nature, it will be seen that the currents resem- 
ble the electric currents resulting from the rotation of a magnet- 
ized sphere in a conducting fluid. The magnetized sphere induces 
in the fluid electric currents, which in turn pass from the fluid into 
the sphere, and from the sphere back into the fluid again, thus 
forming closed paths. Hertz has investigated the simple case 
when the sphere is uniformly magnetized about its axis of rota- 
tion. The figure below is a reproduction of Hertz's diagram in 
illustration of this case. 1 It will be noticed that these currents are 



symmetrical in each quadrant. We can not, of course, look for 
such simple results in the case of a heteorogeneously magnetized 

1 Uber die Induction in rotirenden Kugeln. Inaugural Dissertation, Universital 
zu Berlin, Berlin, 1880, p. 79 and pi. I. Or, Gesammelte Alhandlungen, Vol. I, p. 
115. [In the diagram, the directions of the currents have been reversed, in order that 
the positive directions might correspond with that used in my paper.— Ba.] 



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20 



L. A. BAUER [vol. n, no. i.) 



body like the earth, still we might expect some general similarity 
as actually appears to obtain. Thus, for example, regarding the 
mean of the results in the two hemispheres (the figures in the last 
column of the table), we notice that between the equator and 
parallel of latitude 40 approximately, the currents are, on the 
average, directed downward, or inward, while beyond this latitude 
the current is reversed, and proceeds upward, or outward. For the 
case discussed by Hertz, the latitude in which the direction of the 
current reverses is 34 . 

In the case of the earth, there would seem to be some indication 
that the average current reverses again between the poles and lati- 
tude 6o°. It is not possible, at the present moment, to say how 
reliable this indication may be. 

It is too early as yet to speculate as to the origin of the vertical 
electric currents. The phenomena of atmospheric electricity must 
be examined next, with the view of ascertaining whether they can 
be brought in harmony with those resulting from vertical electric 
currents of the intensity revealed by the previous investigation. 
It is possible that we may be dealing with a phenomenon the result 
of forces equivalent in their action to that of vertical electric cur- 
rents, and that, hence, the non-vanishing of the line integral of the 
magnetic force around a closed curve on the earth's surface may 
not, necessarily, imply the existence of vertical currents, but simply 
the equivalence of the observed effect to that of vertical currents. 

For the present, then, and until further investigations are made, 
it is useless to ask ourselves the question, whether the vertical 
currents are the result of the rotation of the magnetized earth, with 
reference to the ether outside, 1 or whether they are due to the dif- 
ferential rotation of the earth and atmosphere which takes place in 
consequence of the huge atmospheric whirls about each pole. 

It should be pointed out that in order to make more careful tests of 
the non-vanishing of the line integral of the force, it will not suffice to 
consider any one locality, no matter how minute and accurate the 
underlying magnetic survey may be. In order to be able to draw a 
safe conclusion with respect to the earth, as a whole, the test would 
have to be applied over regions in various parts of the earth. It 
might also happen that the vertical current would have its prevalent 
direction reversed at some other time by reason of some sudden 
change in the conductivity of the air or ether. 

1 Professor Schuster, in his article in Vol. I, p. 13, last paragraph, makes a brief 
reference to the currents that might thus be induced in the meridian planes. 



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VERTICAL EARTH-AIR ELECTRIC CURRENTS 21 

Thus, for example, Riicker found from his calculations, using 
the data of the 1886 magnetic survey of the British Isles, that there 
was a downward current of 0.026 ampere per sq. km. in the case of 
one circuit, and one of 0.004 ampere for another circuit; or, taking 
the mean of the two quantities, 0.015 ampere per sq. km. From 
the 1 89 1 survey, however, he obtained from three circuits a down- 
ward current of only 0.004 ampere per sq. km. Looking over the 
figures, as given in the table, we find, between 50 A^and 55 N y an 
average upward current intensity of o. 104 ampere per sq. km. Now, 
Riicker's results do not disprove, as yet, the result from the table, 
for, if we recollect, the tabular quantities simply gave the average 
current-density over the zone considered, and could not be made 
applicable to any special region in that zone. As already stated, 
Riicker was perfectly aware that the negative results reached by him 
by no means disproved the existence of vertical electric currents in 
other parts of the earth. 

It is hoped that the above preliminary results will induce others 
to take up this line of investigation. Only for this reason is the 
present paper submitted for publication. 

The result of this investigation would seem to be that : 

Apparently, an appreciable part of the earth's total magnetism 
can be referred to an effect similar to that of vertical electric cur- 
rents. The average intensity of these currents y for the region between 
60 N and 60 S t would be about one-tenth of an ampere per square 
kilometer of surface. 

A few days after the reading of this paper before the Philo- 
sophical Society of Washington, Professor Bigelow asked me to in- 
form him whether there was any similarity beween his curve 1 giving 
the "vectors of the polar magnetic field as derived from observa- 
tion," and my curve of the vertical electric currents, if the latter 
be inverted. In the diagram below, I present the comparison, and 
have likewise given the curve of mean atmospheric pressure. Al- 
though these curves are not all of them referred to the same merid- 
ian as base line, Bigelow's having reference to the magnetic merid- 
ian, we can, nevertheless, institute a comparison, for the general 
character of the first curve will not be materially changed by trans- 
ference to the true meridian. A striking similarity will be noticed 
between the first two curves, and, as already pointed out in the case 

1 The Earth a Magnetic Shell, by F. H. Bigelow, Am. Jour, of Science, Vol. 
I, p. 88. 



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22 



L. A. BAUER 



CVOL. II, NO. I.] 



of the vertical electric current curve, there is likewise some similar- 
ity with the curve of mean atmospheric pressure. 

What does Professor Bigelow's curve represent? As far as I 
can ascertain from the paper giving the curve, it represents, under 
certain assumptions, the average daily magnetic disturbance vector 
during a certain interval of time at various points along the mean 
magnetic meridian. He says: "The elimination of the polar field 
from the permanent and the electro-magnetic fields consists in tak- 
ing the variations of the daily means of the 24 hourly observations 
on the mean for the months. This gives the three rectangular 
coordinates A H, A D % A V* of the impressed vector that disturbs the 
mean {for the months) from day to day. These values, as they ap- 
pear in the volumes, are transformed into C. G. S. units of the fifth 
decimal place dx> dy, dz; finally, the equivalent polar co-ordinates 
are computed, so that we have s f <*, a, P t the total vector in magni- 
tude, its horizontal components, the angle with the horizon, and 
the angle with the magnetic meridian, respectively." * * * 

The system (shown by the diagram) is a magnetic meridian of 
the earth, with the adjusted vectors at the surface. The notable 
features are the increased vector lengths in the polar regions and in 
latitude io° to 35 °, with diminished vectors at the poles in the 
middle latitude zones and at the equator." He found that these dis- 
turbance vectors lay practically in planes of the magnetic meridians. 



Bigelow's 
Curve. 



Vertical 
Electrical 

Current 

Curve 

(Inverted.) 

Curve 

of Mean 

Atmosphere 

Pressure. 




Assuming, lor the present, the correctness 1 of Bigelow's curve, 
the conclusion to be drawn, seemingly, is: 

That the downward vertical electric current corresponds to an 
increase in the length of the magnetic disturbance vector, while an 
upward current is associated with a decreased vector length. 

1 The writer does not wish it to be understood thereby that he subscribes to 
Bigelow's theoretical views. 



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MAGNETIC WORK AT THE KEW OBSERVATORY, 

RICHMOND, SURREY. 1 

By Charles Chrbb, Superintendent. 

The magnetic work at the Kew Observatory is of a two-fold charac- 
ter. The Observatory serves as a station for obtaining absolute values 
of the magnetic elements and the continuous registration of their varia- 
tion; it also undertakes the testing of magnetic instruments and the 
instruction of magnetic observers. The earliest form of magnetograph 
employed in the Observatory seems to have been on trial in 1851 ; it was 
devised by Sir Francis Ronalds, then Superintendent. The present mag- 
netographs, modifications of the earlier pattern, were erected in 1857 by 
Mr. Welsh, Sir Francis Ronalds' successor. They consist of separate in- 
struments, recording photographically changes in the declination, the 
horizontal force, and the vertical force. The pattern, now known as the 
" Kew pattern," is so well known that description * here is unnecessary. 
The instruments were dismounted for repair during 1874; but with this 
exception have been in almost continuous operation since their first 
erection. The scale values, which are usually adjusted and determined 
once a year, have been kept since 1883 approximately at the following 
values: 

Declination Magnetograph, i cm = 8'.?. 

Horizontal Force " 1 cm = 0.00050 c. g. s. units. 

Vertical " " ,i cm = 0.00050 " " 

The time scale in all the curves has been for many years 
15 mm = 1 hour. 

The Magnetographs are set up in a room in the basement of the 
Observatory, the floor of which is some 10 feet below the ground level ; 
the illuminant used is gas. The magnets are protected from air-cur- 
rents by glass shades with movable baize covers. The shades of the 
horizontal and vertical force magnets contain thermometers, which are 
read twice or thrice daily. A continuous record of the temperature of 
the room is also obtained by means of a Richard thermograph. The 
diurnal variation of temperature is very small at all seasons of the year ; 
but the annual range averages about 20 F. Temperature corrections 
are applied to the horizontal and vertical force records, but the former 
correction is generally very small. 

1 In reponse to several requests received, it is the intention to give in each num- 
ber of the Journal one or more authoritatively prepared reports on the magnetic 
work done at the various observatories. — Ed. 

* See Brit. Assoc. Report, 1859, pp. 200-228. 

23 



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24 CHARLES CHREE [Vol. ii, no. i.j 

Absolute observations x are taken about once a week, in a wooden hut 
situated some ioo yards from the Observatory. The instruments em- 
ployed are a s l A ' ncn d>P circle by Barrow, and a 9 inch unifilar mag- 
netometer by Jones. The latter is employed in obtaining both the hori- 
zontal force and the declination. The dip needles used are 9 cm. in 
length. The horizontal force magnet is a hollow cylinder <)% cm. long 
and 55 % grams in weight, provided with a glass scale at one end and a 
collimating lens at the other. A similar but somewhat lighter magnet 
is used for the declination. 

The distant object used to determine the azimuth in the declination 
observations consists of vertical lines on an obelisk, situated about 450 
yards from the magnetic hut, in the Old Deer Park which contains the 
Observatory. 

It is customary to take the horizontal force observations in the fore- 
noon and the inclination observations in the afternoon of the same day. 

In applying the absolute observations to standardize the photographic 
curves, each month is treated separately. In the case of the declination, 
for instance, measurements are taken of the curve ordinates answering 
to the mean times of the 4 or 5 absolute observations taken during the 
month in question. Attributing an approximate hypothetical value, e.g.. 
1 7 , to the base-line in the curves, and converting the measured ordi- 
nates into minutes of arc by means of the known scale value, one ob- 
tains what may be regarded as provisional curve values of declination. 
From the mean of the differences between these and the corresponding 
results of the absolute observations one finds the error in the assumed 
value of the base-line, and thence its true value for the individual month. 

In the case of the horizontal force the procedure is similar, except 
that use is made of the results-of the entire year in determing the con- 
stant which appears in the subsidiary corrective term in the deflection 
formula. 

In the case of the vertical force, an observed vertical force is obtained 
by combining the observed inclination on any given day with the ob- 
served horizontal force on the same day, the latter being corrected to 
the mean time of the inclination observation by reference to the hori- 
zontal force curve. 

If the curves show any serious magnetic disturbance to have been 
in progress during the time of any absolute observation, this observa- 
tion is omitted from consideration. 

At present, tabulation of the magnetic curves is limited to 5 "quiet" 

days a month, these being selected at the year's end by the Astronomer 

Royal. The mean monthly results obtained from these " quiet " da} r s, 

le corresponding diurnal inequalties for the whole year, for win- 

i for summer, are published annually in the u Proceedings of the 

ill details will be found in Chap. VI, Vol. II, of Stewart & Gee's Elementary 
2/ Physics. 



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MAGNETIC WORK AT KEW OBSERVATORY 



25 



Royal Society," as an appendix to the " Report of the Kew Observatory 
Committee." The mean values of the magnetic elements for the year, 
as deduced from the selected " quiet " days are published in the text of 
the " Report " itself. Last year, for the first time, the " Report " con- 
tained in an appendix a table of recent annual means of the magnetic 
elements at from 30 to 40 of the principal observatories of the world. 
The data were obtained from the publications received by the Kew 
Observatory library, or from correspondence with the directors of the 
observatories. It is the intention of the Kew Observatory Committee to 
publish such a table annually, and they hope that the directors of mag- 
netic observatories will approve this departure, and co-operate to render 
the table as full and accurate as possible. 

Verification Work. 

Between 1853 and the beginning of the present year, there have been 
examined at the Observatory 21 complete self-recording magnetographs 
of the "Kew" pattern, 117 unifilar magnetometers, and 155 dip circles, 
besides a considerable number of separate collimating magnets and dip 
needles. 

The magnetographs are tested in a building adjacent to the Observa- 
tory, provided with the requisite piers for supporting the instruments ; 
attention is given to the accuracy of the clocks, time scales, etc., as well 
as to the character of the magnetic curves obtained. The testing of a 
unifilar magnetometer mainly consists in determining the moment of 
inertia, and the temperature and induction coefficients of the collimat- 
ing magnet, in measuring the deflection bar, and in constructing tables 
for the observer's subsequent use. After the several constants have been 
determined, observations are made to insure that the instrument works 
satisfactorily and gives results fairly accordant with the Kew Unifilar ; 
but hitherto no attempt has been made to obtain a correction so as to re- 
duce all unifilars to a common standard. This is owing partly to the 
large number of observations that would be required to give a satisfac- 
tory correction for the time being, and partly to the uncertainty which 
prevails as to the possibility of securing constancy in any one instrument 
over a long period of time. 

The testing of dip circles and their needles consists chiefly in com- 
paring the results obtained with them with those obtained with the Kew 
needles in the Kew circle. If the two sets of results appear accordant, 
within the limits of the probable experimental error, a certificate is 
issued without any corrections. If the results obtained with a circle and 
needles differ by only 2 or 3 minutes of arc from those obtained with the 
standard instrument, and are fairly consistent amongst themselves, a cer- 
tificate is issued with corrections. If the comparison shows large or ir- 
regular differences from the Kew standard, the instrument is returned 
without a certificate to the maker. In the latter case an attempt is 

4 



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26 CHARLES CHREE [vol. ii, No. i] 

usually made to localize the defect by finding the result of interchanging 
needles with the Kew circle, so as to assist the maker in effecting a cure. 
The magnetic verification work, like the observational, is under the 
T. W. Baker. 

NSTRUCTION OP OBSERVERS. 

umber of magnetic observers belonging to foreign 
itories have received preliminary training at Kew. % 
especially of the epoch when magnetographs of the 
: being first introduced. Of late years the majority 
istruction have been officers of the Royal Navy eon- 
rographic Department ^^ 

on Magnetic Work at Kew Observatory. 

>f scientific papers bearing on the work in all de- 
►ervatory, prior to 1885, is given in Mr. R. H. Scott's 
bservatory." {Proc. Royal Soc., Vol. XXXIX, 1886, 
netic papers in that list will be found under the 
1 Kew Committee," " Ronalds," " Sabine," " Stewart" 
ion with others, " Whipple." Below are the more 
subject : 

> Prof. B. Stewart. Preliminary Results of a Corn- 
Simultaneous Fluctuations of the Declination at Kew 

. Proc. Royal Soc. t Vol. XXXIX, 1886, pp. 362-373. 
Smith. On the Diurnal Variation of the Magnet at 

, August, 1890, pp. 140-145- 

blowing papers in the B. A. Reports, forming part or 

Reports of the " B. A. Committee for the Comparison 

piedc Observations : " 

hippie, pp. 71-74 ; Profs. S. J. Perry and Stewart, p. 75 ; 

and Mr. W. L. Carpenter, pp. 75, 76. 

tewart and Mr. W. L. Carpenter, p. 332. 

Prof. Stewart and Mr. W. L. Carpenter, pp. 28-301 

t Results from the Kew Declination and Horizontal 

phs during the selected " Quiet " Days of the five years 

cts at Kew Observatory during the selected " Quiet " 
ars 1890-95. 

nentioned that Kew Observatory served as base station 
[agnetic Surveys of the British Isles,** by Prof. A. W. 
Thorpe. Phil. Trans, for i$90, pp. 53-32S, and A. 1896, 
. 1-661. 



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ON THE DISTRIBUTION OF MAGNETIC OBSERVA- 
TORIES OVER THE GLOBE. 1 

By Adolf Schmidt. 

The first and most important object being to investigate the main 
features of terrestrial magnetism in its totality, the points of observa- 
tion evidently should be disposed as uniformly as feasible. This holds, 
whatever general problem may be pursued: that of establishing the 
average magnetic condition, or the secular variation ; of observing reg- 
ular oscillations or disturbances. For special problems, which certainly 
should not be neglected, but are, in immediate importance, second to the 
main problem, it may be desirable or necessary to condense stations in 
certain localities, but it is not here contemplated to enter upon the dis- 
cussion of special questions. 

The existing observatories are far from satisfying the above demand. 
The great majority are on European ground; i.e., within 3 V of the 
earth's surface. Of the others, the southern hemisphere contains three, 2 
none of them south of lat. 38 . The immense surface of the Pacific, too, is 
entirely devoid of them. The defects of this arrangement, though they 
have less influence in the case of phenomena (as e.g., the daily variation), 
which depend mainly, though not entirely, on latitude, become more 
noticeable, as the phenomena vary likewise in longitude. It is imma- 
terial whether the results of the observatories be treated simply statis- 
tically and comparatively, or a generalization be attempted graphically 
or by computation. The one way or the other may be better adapted 
to the individual problem, yet upon the selection of the particular 
method to be employed can not depend the maximum reliability of the 
results deduced from the available data in a given case. The lack of 
uniformity in the distribution of magnetic stations would lead us to 
expect rather uncertain conclusions with regard to the earth's magnetic 
action, unless in a special case some law should appear simple and undis- 
turbed. For this very reason, on the other hand, a marked improvement 
in the results might be hoped for, by a judicious disposition of but a few 
stations within the area not covered hitherto. 

Only by computation, however, can a conclusion be reached regarding 
the probable exactness of the results and its improvement through the 

1 A preliminary abstract contributed to the Meteorologische Zeitschrift for July, 
1896. The above partial translation has been prepared for this Journal.— Ed. 

* Of these, the southernmost, Melbourne, is hardly to be counted, since it does 
not publish observations. {Terr. Magn. I, p. 45-46.) 

27 



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26 



CHARLES CHREE 



usually made to localize the defect by finding th« 
needles with the Kew circle, so as to assist the - 
The magnetic verification work, like the <>' 
management of Mr. T. W. Baker. 

Instruction of Oi 

A considerable number of magnetic 
and colonial observatories have receiv 
This was true more especially of the ■ 
"Kew" pattern were being first inti 



Vol. II, No. i.J 

»t because I 

• ^ observa- 

* Orients, 

r* presents 

\-i :e ration of 

::.s of the series 

i he average value 

1 i c sent — e. g., in the 

moment, with a con- 



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DISTRIBUTION OF MAGNETIC OBSERVATORIES 2 g 

the distribution of the points of observation, and hence afford the best 
criterion for the suitability of any particular distribution. I shall give 
only the two most important of these, c and f. They have been com- 
puted for various combinations of the points of observation. These 
combinations are: 

I. The existing principal observatories, omitting a number of Euro- 
pean ones, which, on account of their dense accumulation, could only 
enter with considerably reduced weight into the calculation of any gen- 
eral phenomena; I therefore selected: San Fernando, Stonyhurst, Vienna, 
Pawlowsk, Tiflis, and Katherinenburg (these with somewhat reduced 
weight), and Havana, Toronto, Washington, Irkutsk, Bombay, Batavia, 
Manila, Zikawei, Mauritius, Melbourne. This list is, doubtless, not quite 
complete. Additions to it, however, will probably not materially influ- 
ence the conclusions reached. 

II. The 1 6 observatories just named, and the 13 circumpolar stations 
of 1882-83 ; viz., Point Barrow, Fort Rae, Orange Bay (Cape Horn), Kingua- 
Fiord, Fort Conger, Godthaab, Moltke Harbor (South Georgia), Jan 
Mayen, Cape Thordsen (Spitzbergen), Bossekop, Sodankyla, Miller Bay 
(Nova Sembla), Sagastyr (mouth of Lena). Some of these had to be 
taken with reduced weight on account of their proximity to each other. 

Combinations III to VIII contain, in addition to the 16 observations oi 
group I, such points as seem adapted to become observatory sites. The 
selection of the latter has been made, not only from a theoretical point of 
view, but likewise, as far as possible, from practical considerations. Ex- 
cepting Kerguelen, and perhaps Cape Horn and Point Barrow, hardly any 
of the stations proposed could be objected to as entailing exceptional 
difficulties or cost. 

III. — I . . plus Cape Horn (with double-weight, as also in IV and VII). 
IV. — I . . plus Cape Horn, Cape Town, Wellington (New Zealand). 
V.— I . . plus Honolulu, Tahiti. 

VI. — I . . plus Honolulu, Tahiti, Cordoba (Rep. of Argentine). 

VII. — I . . plus Honolulu, Tahiti, Cape Horn, Cape Town, Wellington. 

VIII. — I . . plus Honolulu, Point Barrow,Tahiti,IyOS Angeles, Callas, Cape 

Horn, Rio de Janeiro, Cameroon, Cape Town, Kerguelen, Tokio, Wellington. 

For these the uncertainty (mean error) of the /?, depending on y and 

*, becomes : 

I. A = ± 1.40 T ± 0.39 if 
II. A = db 0.76 r ± 0.25 9 

III. A = ± 0.82 r ±. 0.34 9 

rv. A = ± 0.70 r ±. 0.29 9 

V. A = ± 1.07 r ± 0.34 9 

VI. A = ± 0.51 r =t 0.29 9 

VII. A = ± 0.37 r ±. 0.26 9 

VIII. A = ± 0.22 r ± 0.21 9 



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30 ADOLF SCHMIDT [vol. n, No. i.j 

These plainly confirm the conjectures made a priori, and show how 
easy it is to obtain a marked improvement by the addition of a compara- 
tively small number of suitably selected stations. Thus the single addi- 
tion of Cape Horn in case III reduces that part of the error dependent 
upon y, by an amount almost equivalent to the effect of the 13 circum- 
polar stations. The coefficient of y depending alone on the position, while 
that of 0, being likewise a function of the number of stations used, ex- 
plains the greater difference in the latter coefficients in cases II and III. 
That in I, c > I shows that the results from this latter group are next 
to useless, for the import of this is that the mean error in the P sur- 
passes the average value of the neglected coefficients. And, as we have 
already seen, the result becomes still more unfavorable by increasing the 
number of unknowns, as must be done in all practical work. At least, 
the five terms of the second order, beyond which we can hardly go for 
the present, will have to be considered. The first term of the error, 
then, depends on <*, instead of y. It is also to be expected that this fur- 
ther loss in accuracy is relatively (and a fortiori, absolutely) greatest in 
the case of I. 

To form a correct estimate of the gain in proceeding from group I to 
II, III, etc., one should bear in mind that if in each group, with its given 
number of stations, the distribution of the latter were the best imagin- 
able, then the accuracy to be obtained would only increase in about the 
ratio of the square root of the number of stations. Taking VIII as a 
comparatively normal state of conditions, we should have for I : 



/\ = I/28: 16 (it 0.22 y it 0.21 $p) = =h 0.29 y dt 0.28 <p, 
instead of ± 1 . 40 y o. 39 <p. 

These figures show very strikingly the unfavorable distribution of 
our present observatories. This is still more strikingly emphasized by 
comparison with an ideal, perfectly uniform distribution. Thus, if there 
were but four observatories, and they were placed at the vertices of a 
regular tetrahedron, we would have A = ± 1.29 y -f o 50 £; for eight 
observatories, situated at the corners of a cube, the first coefficient 
would vanish, giving A = ± 0.35 <p. 

This shows how greatly the present unsatisfactory conditions could 
be improved upon by the addition of a very small number of stations. 
It further appears that new observatories are, above all, needed in the 
southern part of South America, the Central Pacific, and in New Zea- 
land; at the latter especially, as, of all inhabited places of ready access, 
it is the nearest to the south magnetic polar region. These results only 
confirm, qualitatively, our a priori conjectures. That but a few additional 
points, however, should enhance the accuracy of the deductions so con- 
siderably, could hardly have been foreseen. My endeavor in this inves- 
tigation having simply been to obtain some basis for the formation of 



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DISTRIBUTION OF MAGNETIC OBSERVATORIES 



31 



fairly correct estimates, no further significance than to this end should 
be assigned to the figures given. The latter would be slightly modified 
by an extension of the series used, and, in some measure, by alterations 
in the manner of assigning weights, yet all these changes would by no 
means efface — nay, probably, emphasize — the character of the results. 

To the wish that our present system of magnetic observatories may 
soon be adequately supplemented, let us add the hope that the new sta- 
tions be endowed liberally enough to permit not only -the making of 
observations, but also their reduction and presentation in a form suited to 
meet the requirements of modern science ! 



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RESULTS OF MAGNETIC OBSERVATIONS ON THE 
GREENLAND EXPEDITION OF 1896. 

G. R. Putnam, U. S. Coast and Gkodetic Survey. 

The accompanying table gives a summary of the magnetic observa- 
tions made by the writer in connection with the Greenland Expedition, 
under the charge of Professor A. E. Burton, of the Massachusetts Insti- 
tute of Technology. This party was transported to and from its desti- 





/oS 


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u> 9 *• 




V 


*Vm^9*i | 


tkTUB 


(t/T\ 1 \ V 

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A ^ 


* 






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4 






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40 


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nation in Umanak Fiord, by Lieutenant R. E. Peary, in the steamer 
" Hope," and opportunity was afforded to make magnetic observations 
at several stopping-points, going and returning. The route and loca- 
tions of stations are shown in the sketch. The instruments used were 
32 



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MAGNETIC RESULTS 



33 



provided by the U. S. Coast and Geodetic Survey, and consisted of a 
magnetometer of the improved pattern of the Survey, a Kew dip circle, 
chronometers, etc. Most of the stations were identical with or in the 
neighborhood of earlier magnetic stations; those at Godhavn and Hali- 
fax furnishing the most extensive series of observations. A discussion 
of the observations at Godhavn (and at the Whale-fish Islands, to which 
an estimated correction was applied to reduce to Godhavn) extending 
back to 1824, gives the following rough expressions for the change of the 
magnetic declination and inclination (where T is the year for which D 
or I is desired, and -f indicates westerly declination and northerly dip): 
D = + 7i°.54 + o°.i24i (1860-t)— o°.oo367 (1860-t) 2 
I = + 82°.oo -f o°.0246 (1860-t) + o°.ooo32 (1860-t)* 
The accompanying figure represents the curve corresponding to these 
formulas, and indicates the motion of the north end of a freely sus- 
pended magnetic needle as viewed from its center. The half length of 
needle is taken to be 24 inches, or 61 cm. It is of interest as showing 
that the law discovered by Dr. L. A. Bauer, that such motion will be in 
the direction of the hands of a clock, holds good for this Arctic station. 

JXecltmction. West 



V* 



V 



Secular curve for Godhavn. 

In the table, the diurnal ranges are given only for those stations 
where both elongations were observed. In such cases the mean of the 
elongations was taken as the mean declination for the day; otherwise 
the observed .declination was reduced to the mean for the day from such 
comparative data as was available. The diurnal ranges may in some 
cases be abnormal, as for instance at Niantilik on September 18th. An 
inspection of the magnetograms of the U. S. Naval Observatory at 
Washington indicates an unusual magnetic /disturbance on that date. 

A more detailed report of this work, and of the accompanying pendu- 
lum observations, will be published in the Technology Quarterly at Bos- 
ton, Massachusetts. 

5 



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34 



G. R. PCTSAM 



-yaL- IL No. i. 











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LETTER TO EDITOR 



A PROPOSAL WITH REGARD TO AN INTERNATIONAL 
MAGNETIC CONGRESS. 

The necessity of a more systematic and international study of the 
principal phenomena of Terrestrial Magnetism has become apparent to 
many who are working in this field. As a preliminary step to such a 
joint action, it has been suggested that a meeting be called of all those 
interested in the matter, and the year 1900 has been mentioned as an 
appropriate year for such an International Magnetic Congress or Con- 
ference. Allow me in the first place to give two reasons why that par- 
ticular year does not seem to me to be suitable. There will be many 
festivities, exhibitions, and congresses of various kinds to celebrate the 
beginning of the new century, and it is very doubtful whether much 
time will be left for the quiet discussion of a not very sensational subject. 
However, my second reason is more important. A Magnetic Congress 
may possibly, and I hope probably, make some recommendations with 
regard to the reduction of magnetic observations, with a view to a 
greater uniformity in the manner of publication. The year 1900 would 
be the one in which any change in the present system might fittingly 
take place; and it is obviously convenient to give as much time as possi- 
ble to arrange for any modifications of the present system. It would, in 
my opinion, be a great advantage for the Magnetic Congress to meet in 
1899, as there would hardly be sufficient time to make the necessary ar- 
rangements for 1898. 

But who is to call the Congress together? There seems to me to be 
great danger of the proposal falling to the ground, because no one 
likes to put himself forward and suggest some definite mode of action. 
Although I would by preference leave the matter of preliminary organ- 
ization to others, I think all personal considerations should be waived 
for the good of the cause. I would therefore submit the following pro- 
posal to your readers, which possibly may meet with their approval. 
I will ask some scientific man in this country to help me, and similarly 
I propose that the Editor of this Journal should ask some one in 
the United States to assist him. Having thus four men interested 
in the subject, let them meet together during the forthcoming sum- 
mer to talk over the subject, and to ask others — say in France and 
Germany — to act with them. A quite informal committee would thus 
be formed, and this committee would settle the first steps by fixing the 
time and place of meeting. In the meantime, the Journal would no 
doubt be open to any suggestions which its readers would make con- 

35 



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36 A SCHUSTER rvoL. n, No. i.j 

cerning the subjects which should be discussed in the Congress; and it 
would probably be left to the Provisional Committee to settle the final 
program after having considered any proposal submitted to them. 

Such is the outline of a procedure which it seems to me might lead 
to a successful meeting. The committee I suggest would no doubt be 
self-elected, and that is an objection; but what is the alternative? If the 
Congress is to be useful, it is absolutely necessary to have some prelimi- 
nary consideration of the subjects which are to be discussed, and some 
one must take the initiative. The Congress, if it is called together, 
must be as widely as possible open to all those interested in the subject. 
A conference in which those who take part appear as "delegates*' of 
different scientific societies or different countries, would, I am convinced, 
lead to nothing; but it is unnecessary to enter here into the reasons 
which lead me to that opinion. 

It might be difficult for the first four members of the Preliminary 
Committee to come together this year, but it is not necessary that they 
should all four be together at the same time. Thus, if one of the English 
representatives is able to attend the Toronto meeting of the British 
Association, he would probably be able to see one or both American 
representatives during his visit. Now, if one of the latter is able to 
come to Europe during this year, another partial meeting could be 
arranged for here. 

If the proposal I have made does not meet with general approval, I 
shall be only too glad to set it aside in favor of another and better one ; 
but I hope that some means will be found for a full consideration of the 
subject before the end of the century. One of the most important mat- 
ters for consideration at a Congress would be the initiation of some per- 
manent organization to promote international work. It would seem 
desirable that the constitution and method of procedure of such a per- 
manent organization should be fully discussed before the meeting of the 
Congress, and if possible several alternative proposals might be sub- 
mitted to it; for it will be easier for a meeting, which may only have a 
very limited time at its disposal, to decide between different schemes 
which have already received some consideration, than to originate an 
organization after possibly a hasty discussion. There are many serious 
difficulties in the way of any large international scheme ; but I have had 
in my mind for some time already the outline of a scheme, by means of 
which some of the difficulties may be overcome. But the fear of being 
considered too " previous " in this matter stops my entering into details 
at present. 1 Arthur Schuster. 

Manchester, February 7, 1897. 

^he Editor will be pleased to receive suggestions in regard to Professor 
Schuster's proposal. 



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ABSTRACTS AND REVIEWS 



IS THE DECLINATION INDEPENDENT OF THE MAGNETIC 
MOMENT OF THE NEEDLE? 

Lagrange, C. Magnttisme terrestre. La declination (Tune boussole litre et 
h rttat statique, est-elle indtpendante de son moment magnUiquet Ob- 
servations de diclinometres h moments diffirents. Mem. d. l'Acad. roy. 
des sciences, etc. de Belgique. T. LIU. Bruxelles, 1896. 23.5 x 29 cm. 
Pp. 40. 2 plates. 

The Author finds that magnetic needles, having equal magnetic moments, 
and provided with different mountings, march together. Difference in the 
construction of the instruments containing the needles produce no apprecia- 
ble difference in the indications. He solves the differential equation for the 
motion of a free needle, acted upon by a field in which the magnetic me- 
ridian varies in a periodic manner. . When the time of a period is as great 
as one day, it is shown that the needle will not depart from the magnetic 
lines, but will move with them. If the period is 10 minutes and the declina- 
tion in that time changes 40", the departure of the axis of the needle from 
the magnetic meridian in such instruments as the Author used will not ex- 
ceed o'.2. When the suspended needles differ greatly in magnetic moment, 
they give different results. The amplitude of all vibrations like those cover- 
ing a period of several days, as well as the monthly and annual vibrations, 
is greater with magnets having a small magnetic moment The magnetic 
moment was made small by using an unsaturated bar, and also by a nearly 
compensated system of two saturated bars in opposite positions. The ampli- 
tude was in some cases magnified twenty-five to thirty fold. 

The torsional effects of the suspension were found to be inadequate to 
produce such effects. Both silk and metal suspensions were tried, with the 
same results. The convection effects of air-currents were eliminated by 
mounting a single magnet of feeble moment in a tube, which was axially 
coincident with a horizontal diameter of a spherical shell of celluloid sus- 
pended from the fiber of the declinometer. Moreover, the fluctuations were 
shown to bear no relation to temperature fluctuations taking place in the 
observation-room. 

The Author concludes that the effects observed are due to some force other 
than that of the magnetic field proper, and that this action is dependent 
upon the magnetic moment He then develops the equations by which the 
two directing forces may be determined in direction and in intensity. 

Francis E. Nipher. 
37 



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38 REVIEWS [vol. 11, No. i] 



OBSERVATIONS MAGNETIQUES EN SUISSE, EXECUTEES EN 1895.* 

Cet opuscule contient les travaux preliminaires des deux auteurs, MM. 
les docteurs van Rijckevorsel et van Bemmelen, qui se sont propose de me- 
surer V influence de la hauteur audessus du niveau de la mer sur les con- 
stantes du magn£tisme terrestre. Le Righi, presentant les avantages d'isole- 
ment, de hauteur et de constitution geologique favorable, fut choisi comme 
point d' observation. II s' agit d' en sonder la constitution — probablement 
nonmagn£tique. Deux cercles, V un de treize, V autre de six stations de 
m£me niveau, furent £tablies alentour de la montagne. Leur distance moy- 
enne fut de 6 kilom. Les instruments et les m€thodes d' observation, dont 
on trouve dans la brochure une description d£taillee, furent les memes dont 
se servit M. van Rijckevorsel dans les Pays-Bas. Quoique 1* on ait constam- 
ment d£termin6 la torsion du fil, les auteurs trouvent neanmoins, qu' on y 
perd trop de temps sans gagner un surcroit d' exactitude qui permette de 
reoommander cette operation. II ne s' est guere present^ de perturbations 
considerables a 1' exception d* un jour, le 29 mai. P. W. 



THE NEW COAST AND GEODETIC SURVEY MAGNETOMETERS. 

We have the pleasure of acknowledging the receipt of a photograph ol 
these new instruments from General W. W. Duffield, Superintendent of the 
Survey. The following description is taken from Appendix No. 8 of the Re- 
port for 1894, p. 275: 

In their general form these instruments are similar to those that have 
been in use in the Survey for some years, an illustration of which will be 
found in United States Coast and Geodetic Survey Report for 1881, Appendix 
No. 8, plate 36. The new instruments are a little larger than the old ones, 
and are improvements upon them in details of design, and especially in sta- 
bility and perfection of workmanship. 

The new coMmating magnets are octagonal in form. 

The stirrups in which the magnets are suspended are very light, and 
made to support the magnets on two of their plane surfaces. The magnets 
can be suspended in the stirrups with scales accurately vertical, either erect 
or inverted at once, and the inertia ring can be accurately balanced upon the 
magnet with equal facility. With the old cylindrical magnets these opera- 
tions were difficult and very trying to the patience of the observer. By 
means of a small rod attached to the stirrup^ the point at which the suspen- 
sion fiber is fastened is raised a considerable distance above the center of the 
magnet. The effect of dip in different localities to displace the magnet from 
its horizontal position is thus overcome, and the sliding ring used in the old 
instruments is unnecessary in these new ones. The oscillating mass is always 
the same, and consequently its moment of inertia also. Another new feature 
is the black velvet screen connecting the telescope with the suspension box. 
This does away with the glass window usually placed in the suspension box 
between the telescope objective and the objective of the magnet It also 
cuts off all stray light between the telescope and the magnet, and renders 
the illumination of the magnet scale a matter of great ease. 

1 Magnetische Beobachtungen imjahre, 1895, ausgefiihrt durch Dr. van Rijcke- 
vorsel und Dr. van Bemmelen. 



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REVIEWS 39 



SECULAR VARIATION OF THE EARTH'S MAGNETISM IN THE 
UNITED STATES. 

The Journal has been favored with an advanced copy of the following 
article, forming Appendix No. i, of United States Coast and Geodetic Survey 
Report for 1895, W. W. Duffield, Superintendent, entitled: 
Secular Variation of the Earth's Magnetic Force in the United States and 

in some Adjacent Foreign Countries. Report by Charles A. Schott; 8th 

edition, with 1 chart and 3 plates. Washington, 1896. 4to; pp. 167-320. 

The following abstract has been kindly furnished by the Author: 

" In this report we have presented, in a condensed form, the results of 
the latest researches by the United States Coast and Geodetic Survey respect- 
ing the secular variation of the earth's magnetic force within the limits, or 
close thereto, of the United States, and brought up to date of March, 1896. Its 
distinguishing feature from preceding editions is the more general treatment 
of the secular variation of the declination, together with the concomitant 
variations of the dip and intensity. 

" We find here collected, for such selected localities as give promise to ad- 
vance our knowledge of the secular changes in the distribution of magnet- 
ism within the geographic limits set here, all known observed and accessible 
data, whether of declination, dip, or intensity, from the earliest to the present 
time. 

"Before this, the discussions of the variations of the declination and of 
those of the dip and intensity were kept separate, which proceeding, in a 
measure, cut us off from taking advantage of any mutual support we may 
derive from a joint consideration. This, of course, was a necessary outcome 
due to the fact that the data for the changes in the declination alone were 
sufficiently extensive to give us any hold on the phenomenon. On the 
other hand, the time range of the dip observations at American stations is 
unfortunately very short, and were it not for a few observations — about a 
dozen and a half — in the eighteenth century, we should have been entirely 
dependent on observations made in the current century, and for the most part 
after its first quarter had already elapsed. With respect to changes in intensity, 
the time covered is still shorter, but here the researches in all countries are 
equally restricted. 

" To gain space, the references to the observations are not as full as in 
preceding editions, except in those cases where either old observations have 
been discovered or when new data are introduced. The variations are still 
represented by simple sine formula, except when the data for their proper 
evaluation were insufficient, as is the case with the variations of the dip and 
intensity, which therefore include but two periodic expressions. The non- 
periodic formulae involve the first and, generally, also the second power of 
the time; the epoch common to all formulae is the beginning of the year 
1850. It can not be pretended that these simple formulae do actually repre- 
sent the respective magnetic variations, not even for so (relatively) short 
a time as one or two centuries ; they ever require small changes or improve- 
ments to make them conform to the latest (or indeed all) observations. It 
is perfectly certain, for the American observations, at least, dating from the 



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REVIEWS 41 

time of the discovery of the New World and ranging through the sixteenth 
and part of the seventeenth centuries, that they are difficult if not impossible 
to reconcile with the results from our simple periodic formulae when thus un- 
duly extended into the past. This difficulty we may hope to surmount here- 
after, but it must exist so long~as we are compelled to employ mere interpola- 
tion formulae to represent a natural phenomenon which is undoubtedly of an 
extremely complex character. It is therefore very essential that the limits of 
applicability given in the paper to each expression be not transgressed, un- 
less such extension in time, backwards or forwards, is supported by newly 
discovered data or by new observations. 

" For the individual and generalized results contained in this appendix, 
the reader must be referred to the paper itself, which is adequately illus- 
trated with a chart embodying general conclusions and a series of diagrams 
of secular variations of salient features." 

The plates opposite present the curves described by the north end of a 
freely suspended magnetic needle, as viewed from the center of the needle. 
The scale employed in the Report has been reduced one-half, the Author 
using the same angular scale for all the curves given. 

The stations were selected by the Author as typical ones for the regions 
included in his researches. It will be seen that more than half of the curves 
proceed clockwise. Some of the remainder do not extend over a long enough 
interval to exhibit a decided direction, while others appear to have the general 
motion reversed. The stations indicating the reversed motions are located 
along the western coast of North America. That a reversal or a small loop might 
be expected for this region and the Pacific Ocean had already been pointed out. 



MAGNETIC OBSERVATIONS AT HIGH ALTITUDES. 
In view of the valuable work bearing on this subject, which Drs. van 
Rijckevorsel and van Bemmelen.are carrying on in Switzerland, it will not be 
amiss to call attention to some extremely interesting observations which Mr. 
E. D. Preston, Assistant of the United States Coast and Geodetic Survey, made 
in the Hawaiian Islands during 1892. He was engaged at the time in observ- 
ing for variation of latitude. An account of the work will be found in Ap- 
pendix No. 12 of the United States Coast and Geodetic Survey Report for 1893. 
From the table below it will be noticed that the highest station was at an 
elevation of 3,981 meters above sea-level, namely, at Waiau, on the summit of 
Mauna Kea, an extinct crater. The instrumental outfit consisted of the Coast 
and Geodetic Survey Magnetometer No. 1 1 and a Kew dip circle. The declina- 
tions are the means of the western and eastern elongations ; no reduction to 
mean of day, in the absence of a magnetic observatory, could be applied to 
the results. In the last line of the table will be found the mean values of the 
three coast stations, Nos. 1, 6, and 7. The additional data given in this table, 
not contained in the publication cited, has been supplied by Messrs. Schott 
and Preston. Without a more careful study no safe conclusion can be drawn, 
though it would appear that the total force, as well as the components, with 
the exception of the easterly, decreased when the high altitudes were reached. 
Mr. Schott informs the Editor that the Coast and Geodetic Survey has a 
number of stations in the United States at still greater altitudes. The results 
(not yet published) " do not exhibit any marked deviations either in direc- 
tion or intensity from ordinary ones met with in level countries." 

6 



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42 



REVIEWS 



[Vol. II, No. i.] 



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NOTES. 



EDITORIAL NOTICE. 

With the March, 1897, issue, this Journal, devoted exclusively to Terres- 
trial Magnetism, and allied subjects, such as Earth Currents, Auroras, Atmos- 
pheric Electricity, etc., enters on its second volume. The hearty co-operation 
extended, and the warm encouragement received from all sides, are the surest 
proof that the inauguration of this Journal has met a keenly felt want Doubt- 
less never before has such enthusiastic interest been taken in this most elusive 
subject 

This Journal, as is abundantly shown by the Table of Contents of Volume 
I, has become the international organ for making known the latest achieve- 
ments. 

The Editor having been appointed Assistant Professor of Mathematics 
and Mathematical Physics at the University of Cincinnati, the office of publi- 
cation has been transferred to this institution. In all other respects, Volume 
II will resemble Volume I. There is already every indication that the coming 
volume will be as interesting and as valuable for future reference as the past 
volume. 

// is earnestly hoped that every one who has the advancement of this subject 
at heart will become a subscriber. The Editor, as in the past, bears the entire 
financial responsibility. But a few copies of Volume I are left, the edition 
having been strictly limited. It will, consequently, not be long before it will 
be impossible to fill back subscriptions. 

Avis! Le numero de Mars, 1897, commence le tome II de ce journal 
exclusivement destin6 au majgneiisme terrestre et a ses allies — les courants 
terrestres, les aurores, V electricity atmospherique, etc. 1/ active collaboration 
et T encouragement cordial recus de tous cdtes est preuve sure de ce que ce 
journal est venu combler une lacune devenue tres- sensible. Sans doute cette 
tranche delicate des sciences naturelles n 'a jamais ete 1' objet de tant d' interet 
et d' enthousiasme qu' on y porte de nos jours. Le contenu de notre tome I 
demontre suffisamment que le "Journal" est devenu 1' organ e international 
pour la publication des resultats les plus recents. 

On continuera de publier les memoires dans la langue dont se serviront 
MM. les auteurs, pourou qu' il soit possible de V imprimer en caracteres latins 
et que ces messieurs n' en aient pas eux-m€mes desire la traduction. 

Le reclacteur ayant €t€ nomm6 "Assistant" Professor de Mathematiques et 
de Physique theonque a 1' Universite de Cincinnati, le bureau de publication 
a €t€ elabli dans cet institut. Ce sera le seul changement. Les memoires 
promis et recus jus qu' ici nous permettent d' annoncer que le tome prochain 
sera tout aussi interessant et donnera d' aussi precieux renseignetnents que 
celui qui vient de paraitre. 

Nous espirons que tous ceux qui s' inttressent au diveloppement de la 
science du magnitisme terrestre y concourront en s 1 abonnant a notre journal. 
Le r6dacteur seul en porte la responsibility financiere. 

A cause de 1' edition limitee du tome I et du peu d' exemplaires qui en 
restent, la livraison des numeros precedant celui de Mars 97 ne tardera pas a 
devenir impossible. 

Zur Beachtung! Mit dem Marzhefte 1897 tritt diese Zeitschrift, welche 
ausschliesslich dem Erdmagnetismus und verwandten Erscheinungen, wie 
Erdstromungen, Nordlicht, atmospharische Electricitat u. s. w., gewidmet ist, 
in ihren zweiten Jahrgang ein. Dass ihr Erscheinen einem deutlich gefiihlten 
Bediirfnisse entsprach, beweist die allseitig gewahrte lebhafte Teilnahme und 

43 



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44 



NOTES IVol. ii, N-o. i.j 



Mitwirkung der Fachleute. Sicher ist nie zuvor das Interesse anmnserem 
9chwierigen Gegenstande so stark hervorgetreten, wie gerade jetzt Dieses 
"Journal" ist, wie das Inhaltsverzeichnis des ersten Jahrganges zur Genuge 
zeigt, zum in ternationalen Organ fur die neuesten Leistungen . auf diesem 
Gebiete geworden. Mittheilungen werden wie bisher in der Spracbe der 
Verfasser erscheinen, sofern sich dieselbe mit lateinischen Lettern drucken 
lasst und die betr. Herren nicht selbst eine Cbersetzung wiinschen. 

Da der Herausgeber inzwischen an der Universitat von Cincinnati als "As- 
sistant " Professor der Mathematik und der mathematischen Physik angestellt 
worden ist, wird die Redaktion und Expedition nunmehr nach dieser Anstalt 
verlegt werden. Abgesehen hiervon ist keinerlei Anderung beabsichtigt, und 
lassen die bereits versprochenen und eingesandten Artikel schon jetzt erken.- 
nen, dass unser neuer J ah r gang dem ersten an Interesse und Wert als Nach- 
schlagebuch nicht nachstehen wird. Financiell ist der Herausgeber wie 
bisher allein verantwortlich. 

Geben wir tins der ernstlichen Hoffnung /tin, alle die, welchen die F'drde- 
rung unser es Faches am Herzen liegf, zu unseren Abonnenten zu zahlen! 

Nur wenige Exetnplare des ersten Jahrganges sind noch vorhanden, da 
die Zahl derselben von vornherein eine genau beschrankte war. Es wird 
paher binnen Kurzem nicht mehr moglich sein, friiher erschienene Nummern 
zu liefer n. 



MAGNETISCHE LANDESAUFNAHME DER NORDDEUTSCHEN 

GEBIETE. # 

Eine magnetische Landesvermessung wird seitens des magnetischen 
Observatoriums zu Potsdam geplant Dieselbe wird sich zunachst auf die 
norddeutschen Gebiete erstrecken bei einer Dichtigkeit des Netzes von 40 km. 
Die Vermessung wird circa 5 Jahre in Anspruch nehmen. 

Ein Punkt von allgemeinem Interesse, der auch als Gegenstand der Be- 
rathungen in Paris von Dr. Eschenhagen vorgeschlagen war, betrifft die Aus- 
wahl der Stationen. Nach Dr. Eschenhagen's Plane werden namlich fiir das 
ganze Vermes^ungsgebiet nur eine geringe Zahl (circa 30-40 Stationen) von 
Punkten derart festgelegt, dass eine Wiederauffindung und Wiederbenutzung 
auf moglichst lange Zeit gesichert ist. Man wird hierzu Orte wahlen in grosserer 
Entfernung von Stadten, von deren Erhaltung auch die trigonometrische 
Vermessung ein Interesse hat, und die durch sichere Aufstellung von Steinen 
auffindbar sind. 

Bei der grosseren Zahl der Stationen wird man auf diese Wiederauffindung 
nicht den gleichen Werth legen und dadurch einen schnelleren Fortschritt 
der Vermessung erzielen. In den erst erwahnten Hauptpunkten wird im 
ersten und im letzten Jahr die Vermessung besonders exact beobachtet und 
daraus die Sacular- Variation abgeleitet werden. 

Die Anlage solcher Hauptpunkte ist von Nutzeu bei Wiederaufnahme 
aller spateren Untersuchuugen ; wenn z. B. softer andere Beobachter im 
dichteren Netz beobachten wollen, so haben sie nur nothig an einigen im 
Gebiet liegenden Hauptpunkten sorgfaltige Bestimmungen zu raachen, um 
einen sicheren Auschluss an die altere Vermessung zu erzielen, indem sic 
alle ihre Beobachtungen dann durch Ableitung der DifFerenz ieder Station 
gegen die Hauptpunkte auf dieselben beziehen. Man sieht, dass auch die 
Mangel, die durch Benutzung verschiedenartiger Instrumente entstehen, hier- 
durch ausgeglichen werden konnen. 



Corrigenda. Vol. I, p. 47, eighth line from bottom, read Galton instead of 
Dalton. Bd. I, S. 188, 7. Linie von oben lies —15/8 statt 15/18. 



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VohAne 11 



iHE NEW YORK 

PUBLIC LIBRARY 



ASTOR, LENOX AN» 
TILDEN FOUNOATIONa. 



Number 2 



Terrestrial Magnetism, June, 1897 



THE EARTH, A GREAT MAGNET. 1 

By Dr. J. A. Fleming, M. A., F. R. S., 

Professor of Electrical Engineering in University College, London. 

When the invitation came to me to address this evening a lecture to 
a Liverpool audience in accordance with a usual custom during meet- 
ings of the British Association, the natural desire arose to select some 
subject which should have a more or less close relation to the in- 
dustries and commerce of your great city. With a choice somewhat 
limited by the nature of my own studies, it seemed to me, however, 
that we might find an appropriate topic in discussing, for a brief 
hour, the fact of the earth's magnetic properties, and the history of 
the discoveries by which that supremely important knowledge has 
been gained. 

To do this with advantage, we shall approach the subject through 
the avenue of some experimental demonstrations intended to place 
you in possession of the elementary principles of magnetic science. 

I hold in my hand a specimen of a kind of iron ore, the scien- 
tific name for which is magnetite ■, but which familiarly is called lode- 
stone. This particular sample came from a place called Magnet 
Cove, in Arkansas, in the United States ; but it is very widely dif- 
lused over many regions of the earth. This brownish stone would 
hardly attract your attention at all if you saw it lying in the road, 
but it has been known for many centuries to possess unique powers, 
and these can very easily be rendered evident to you. 

First of all, let us dip the lodestone into a little heap of iron 
screws or nails, and note the fact that at one or more points on its 
surface it possesses the power to attract these objects. It will not 
pick up pins made of brass wire, but a bundle of sewing-needles 
yields easily to its blandishments, and one large lodestone will 

1 A lecture delivered to the workingmen of Liverpool, Sept. 19, 1896. 

[For many years it has been the custom to have a popular experimental or illus- 
trated lecture delivered during the meeting of the British Association for the Ad- 
vancement of Science, addressed especially to the artisans of the town in which the 
meeting takes place. The above lecture is the text of the discourse delivered by Dr. 
J. A. Fleming, at Liverpool. The lecture was profusely illustrated by experiments, 
lantern slides, and projections thrown on the screen by the aid of vertical and hori- 
zontal lime-light lanterns. The lecture was delivered to an enormous audience in the 
Picton Hall. It appears in this Journal in full for the first time. — Ed.] 

2 45 



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^6 /• d. FLEMING [vol. ii, no. *.) 

readily lift up another smaller one, when the attractive portion or 
end of the first is brought near to the second. 

If the lodestone is dipped in iron filings, these cling to all the 
edges and points of it, and the marvelous stone immediately grows 
a beard, as it were, fringed all round with closely-clustering parti- 
cles of iron. 

John Baptista Porta noticed that fact in 1589, but he hardly car- 
ried knowledge further than it had been taken in the well-known 
Latin poem of Lucretius, written sixteen centuries before; and it is 
only in the writings of Nicholas Cabaeus of Ferrara, in 1629 A. D. f 
that we meet witha diagram which clearly records the observed 
facts that these filings cling, not uniformly all over the stone, but 
at certain predominant places, which afterward became called the 
poles. The attractive powers of this stone are not, however, its 
most remarkable property. 

It is impossible definitely to assign a date to the first knowledge 
that if an elongated piece of lodestone is freely suspended horizon- 
tally, either by floating it on water in a bowl or by a thread tied 
round it, it places itself in a definite position, to which it returns if 
disturbed. The oldest picture of this experiment represents the 
lodestone placed, as one writer says, "like a sailor in a boat,*' and 
floated upon the surface of water in a larger vessel. The moment 
we repeat this experiment, we can ascertain two facts — one, that 
there is such a directive tendency in a suspended stone; and next, 
that the two ends of the stone have different properties, and act dif- 
ferently to the same end of a second fixed lodestone. 

Whatever Asiatic peoples or early nomad tribes may, in the dawn 
of history, have discovered concerning this directive power of the 
lodestone, or its " verticity," as Gilbert afterwards called it, there is 
no trustworthy evidence that the natives of Europe had any ac- 
quaintance with it before the twelfth century of our era. The ear- 
liest actual mention of it in English was in the writings of Alex- 
ander Neckam in 1200, A. D. In 1269 we find a very important 
contribution made to accurate knowledge of facts, as compared with 
useless scholastic speculations, in the celebrated letter of Peter Pere- 
grinus, or Peter the Pilgrim (not to be confounded with Peter the 
Hermit), who was a soldier-monk serving in the army of Charles of 
Anjou, the brother of Louis IX of France. This letter, indited on 
the 1 2th of August, 1 269, in the trenches at the siege of Lucera, con- 
tains the clearest statement ot the law of behavior of magnet poles 
to each other. 



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THE EARTH, A GREAT MAGNET 47 

Peregrinus describes, in this letter, the construction of a true mag- 
netic compass, as we have it at the present day, and he was perfectly 
familiar with the power of the lodestone to communicate its proper- 
ties to an iron or steel needle. He knew that on stroking a steel 
needle over the lodestone pole, a communication of its attractive and 
directive powers will be made. This fact formed the starting-point 
for new investigations, and Peregrinus added another of immense 
value in its influence on magnetic theory; viz., that we can not sepa- 
rate the poles of a lodestone one from the other. 

The experiment with the floating lodestone compelled Pere- 
grinus to definitely name the poles of the magnet. He says: " The 
stone so placed will turn in its little vessel until the north pole of 
the stone will stand in the direction ot the north pole of the heavens, 
and the south pole of the stone in that of the south pole of the 
heavens, and if it be removed from this position, it will return 
thereto by the will of God." ' 

Peregrinus thus initiated that nomenclature which has endured 
to the present day, and the custom of calling the end of the sus- 
pended lodestone which directs itself to the north, the north pole, 
and to the south, the south pole. 

He then went on to demonstrate that it is impossible to sepa- 
rate the north pole from the south pole, and that if a lodestone is 
broken in half, each half immediately possesses two opposite and 
perfect poles. We can try that experiment very much more easily 
with a fragment of magnetized steel, and the logical issue of this is to 
lead us to conclude that every particle of the lodestone or of the 
Steel magnet is a complete lodestone or magnet. 

At this stage it is necessary that your attention should be drawn 
to the difference in magnetic properties between iron and steel, a 
difference first noticed by Porta. Both iron which is chemically 
pure, and iron alloyed with carbon in the form called steel, can be 
magnetized ; in fact, iron is susceptible of a higher degree or inten- 
sity of magnetization than many kinds of steel : but the steel re- 
tains it more firmly than the iron against mechanical shocks, such as 
twisting, hammering, or bending. I show you the feeble power of 
iron to retain acquired magnetic polarity by magnetizing this iron 
wire, and then giving it a little twist. That twist is sufficient to 

1 Park Benjamin. The Intellectual Rise of Electricity, p. 172. The reader 
will find in this treatise a most careful historical survey of magnetic discovery, and to 
it the present writer has been indebted for many of the above and following histor- 
ical facts. 



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4 v /. A. FLEMING 1vol. ii, no. 2.3 

deprive it of all sensible magnetism. In magnetic language, pure 
iron is called "soft iron." There ar£ certain kinds of steel called 
magnet steel, which have a special composition, aiding them in ac- 
quiring strong magnetization, and in retaining it when acquired. 

So much, then, being said for the properties of the lodestone in it- 
self, let us review a few of the facts connected with the conveyance 
of its powers to soft iron. Far back into classical times it had been 
known that iron brought in contact with the lodestone acquired the 
same powers while in touch with it. Early Phrygian iron miners, 
settled in Samothrace, were acquainted with the fact that the lode- 
stone could lift up an iron ring, and this in turn could lift up an- 
other, and so on, the iron acquiring temporarily magnetic powers. 

Magnetic quacks must evidently have flourished in these early 
days, since these Samothracian rings of iron were even prescribed 
as a remedy for gout in the fingers, and priests of Samothrace, in 
514 B. C, appear to have driven a trade in magnetic cure-all rings, 
just as certain individuals, at the present day, do in magnetic 
belts. 

It was found that a lodestone could be improved in lifting qual- 
ity by furnishing its ends with iron caps, and these caps were 
called the armor or armature of the lodestone, a term which has 
survived to the present day in connection with dynamo machines. It 
was Peregrinus who probably first stated that a fragment of iron 
wire held near a lodestone becomes itself magnetized by induction, 
as it is called, and then places itself in a certain direction or posi- 
tion in space. It remained, however, for that ingenious philoso- 
pher, Descartes, whose grim physiognomy hardly suggests the ex- 
treme nimbleness of his intellect, to grasp the idea that the lodestone 
affects all the space around it and along certain definite lines. 

Nearly one hundred years before that time, Gilbert had called 
the region round about the magnet, within which its influence is felt, 
its "orb of virtue/' and represented little fragments of iron as setting 
in certain positions near a spherical lodestone. 

Slowly, however, the idea grew up, not finally perfected until the 
time of Faraday, that the effect of the lodestone on iron and mag- 
nets not in contact with it could only be explained by the concep- 
tion of a magnetic force distributed along curved lines in the space 
around the lodestone. 

Descartes gives a most curious and correct diagram of what he 
considered to be the direction of these lines of magnetic force pro- 
ceeding from a lodestone ball. Before turning to consider the epoch- 



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THE EARTH, A GREAT MAGNET 9 

making work of Gilbert, let us briefly examine the facts connected 
with the magnetic force of a magnet. 

If one magnet, movable round its center, is placed in the neigh- 
borhood of another, we have already seen that there is a direction- 
imposing influence acting on the movable magnet. If we carry a 
small fragment of magnetized steel round a larger fixed magnet, we 
find at all points of its journey that the small magnet takes a partic- 
ular direction with respect to the larger one, and this indicates the 
direction of the magnetic force at that place. 

If instead of this we scatter steel filings over a magnet, each 
little fragment is magnetized by induction, and sets itself in a cer- 
tain direction under the influence of the magnetic force. The whole 
collection of filings delineates certain curved lines, called lines of 
magnetic induction. I particularly wish you to see the nature of 
the field of force, as it is called, round a sphere having a magnet 
placed in it, and to note that a small magnet carried round the space 
always places itself so as to be in the same direction as these lines 
of magnetic force. 

You must therefore think of a magnet, whether lodestone or 
steel magnet, as surrounded by this " orb of virtue," to use Gilbert's 
phrase, or, in Faraday's language, by its magnetic field, consisting 
of the curved lines of magnetic force. And more, you must think 
of these lines of force as closed loops, so that they must be pic- 
tured as coming out of one pole of the magnet, passing through the 
circumjacent space, and entering it again at the other pole, and so 
completing their circuit, partly inside and partly outside the magnet. 

Before continuing to examine the historical progress of mag- 
netic knowledge, it will be convenient to conclude the description 
of the work of Peter Peregrinus by a mention of the inventions he 
made in perfecting the magnetic compass. The use of a floating 
lodestone, or steel needle magnetized by touching against a lode- 
stone, to determine a constant direction for the purpose of naviga- 
tion or travel, lies far back in antiquity. 

During the Middle Ages the territory about the Baltic Sea was 
occupied by the races of Finns, the Esthonians, and the Lapps. 
The Finns were a gloomy, earnest people, showing on their faces 
marks of their Tartar connection, and relation to the far-distant 
Chinese. They were the earliest iron-workers in the north of Eu- 
rope, and Finnish swords anciently had a reputation almost equal 
to that of the famous blades of Toledo. In the Baltic lies the island 
of Gottland, and in the twelfth century it had, as one of its princi- 



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xo / A FLEMISG tdc n 5« i.; 

pa! cities. WLsr/ay. a place of meeting for the vessels of a3 trading 
nations. Such influence had this place in controlling matters con- 
n -cted with navigation that the Ordinances and Laws of Wisbuy 
formed an almost universal Code of Marine Law, evidences of which 
are imbedded in our modern codes. In the Middle Ages it was a 
great center of trade and point of contact for all maritime nations. 
It has been urged by some writers that it was from this great sea- 
faring center that, at the beginning of the twelfth century, a general 
knowledge spread over Europe of the use of the lodestone in navi- 
gation, A great step, however, separates the use of a magnet 
merely for the pupose of ascertaining the north and south direction, 
and the method of obtaining by it the correct "bearing" of any ob- 
ject or direction of the ships head. 

Whatever may have been done before. Peregrinus at any rate 
brought inventive power to bear on the subject- He added a pair 
of sights and a graduated scale to the floating lodestone. and he 
improved the compass made with a pivoted steel needle by the addi- 
tion of an azimuth bar and scale, so that it could be used to obtain 
the angular distance of any object from the meridian line* He thus 
invented the means by which, not a merely north and south direc- 
tion, but the direction of a ship's head, could be ascertained exactly, 
as we do at the present day. There were, however, two well-known 
features of the modern compass card which the instrument of Pere- 
grinus lacked. Those were the card divided into thirty-two 
"points," each having its appropriate name, to repeat which in or- 
der is called " boxing the compass," and the fixing of this card to 
the needle so that the card and needle turn together, the bearing of 
the ship's head being ascertained from the position of the card with 
reference to a fixed point on the case. 

It was probably the Italian Gioja who first added the card, and. 
we learn from a commentator of Dante, writing in 1380, that at that 
date the card, bearing the well-known star-like device called the 
" Rose of the Winds," painted on a circular card fixed to and turn- 
ing with the needle, had already been invented. 

Hence we may say for certain that at the end of the fourteenth 
century the magnet compass, as we have it now, was in general use, 
although time has added many improvements, and, latest of all, Lord 
Kelvin has given to us probably the most perfect form yet made. 

The word compass is an old English word, signifying a circle. 
" My green bed embroidered with a compass " is mentioned in the 
will of Edward, Duke of York, who died in 14 15. 



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THE EARTH, A GREAT MAGNET 5I 

The well-known instrument for describing a circle is called a com- 
pass or pair of compasses. To encompass means to surround as by a 
circle, and most of you at some time or another have seen a public 
house with the sign of the " Goat and the Compasses," which anti- 
quarians tell us is only a corruption of the old pious house-motto, 
" God encompasses us." Hence the magnetic instrument takes its 
familiar name from the circle of degrees or points which Peregrinus* 
or Gioja added to enable it to indicate the angular distance of an 
object from the meridian. 

So far, I have said nothing about the theories which had been 
formed as to the cause of the directive properties of the magnet. 
Those who came before Peregrinus had a general notion that the 
pole star governed the motion of the magnet. He knew that the 
pole star varies in position, and he expressly states that the needle 
points, not to the pole star, but to the poles of the heavens. But 
whether attributing the orientation of the magnet to the pole star, 
or the celestial poles, or to magnetic mountains in the Northern re- 
gions, no one had yet solved the secret of the directive power until 
Dr. Gilbert turned his mind to the subject, and did not leave it until 
he had set the whole science of magnetism on a solid basis of ex- 
periment and scientific inference therefrom. 

William Gilbert, born at Colchester in 1540, was the author of 
that great treatise "On the Magnet," which has given him imper- 
ishable fame. Though a scholar, physician, and courtier, attached 
to Queen Elizabeth's household as body physician, and finally pres- 
ident of the Royal College of Physicians, we know of him com- 
paratively little, except in the record of that scientific work which 
has come down to us from him in the pages of two books printed 
three hundred years ago. But the contribution which he made to 
the subject was remarkable, and it was nothing less than the new 
idea that the whole earth itself is a great magnet, and the magnetic 
forces which act on all little magnets on its surface emanate from the 
globe itself. To understand the manner in which Gilbert ap- 
proached the subject, we must realize that his great contemporary, 
Galileo, in Italy, was then marching forward in the triumphant ca- 
reer of discovery which followed his invention of the astronomical 
telescope, and that the minds of all intelligent men in that day were 
keenly interested in the contest raised by the enunciation of the 
doctrine of Copernicus, that the earth was not at rest in the center 
of the universe, but revolves round the sun with a double mo- 
tion — one of rotation round the sun, and of rotation round its own 



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52 J* A. FLEMING [vol. 11, No. 2.] 

axis. Proof was being eagerly sought to support or disprove this 
new theory. 

The great obstacle to the reception of this doctrine, apart from 
theological dogmas, was the difficulty of understanding how the 
earth was sustained in its orbit and its rotation maintained. Gil- 
bert entered the lists with some ideas that the earth possessed mag- 
netic properties, and was sustained and moved by the magnetic power 
of other celestial bodies. Like many other investigators, he was 
led by a wTong theory to new facts. He began by making a little 
model of the earth out of a lodestone, which he called an earthkin, 
or terrella, and with this he experimented. He poised upon the 
surface of his little globe small iron needles or little magnets, and 
noted that wherever placed the little needles pointed to the 
poles of this miniature earth. Regarding intently this fact, that 
poised magnetized needles set themselves to point in the direc- 
tion of the poles of the real earth, and that his little needles on 
their earthkin cut of lodestone did the same, he was led to make 
the grand induction that our globe itself acts as one great lodestone 
or magnet, and his idea was that the mineral we call lodestone is 
but, as it were, a fragmenc of the true mother earth, and, like a " chip 
of the old block," has all the properties in miniature which its great 
original possesses in the mass. 

Gilbert's particular astronomical notions were soon stripped 
away ; but inside the husk of theory there was the kernel of a valu- 
able truth, and it remained as the essence of what Gilbert gave us 
in his great book, 4< De Magnete," published in 1600, A. D. 

All that has been done since that date has been to build up an 
irrefutable body of proof, some part of which we shall presently 
review ; but Gilbert with his lodestone balls first grasped the essential 
idea that the earth we live on has magnetic properties as a whole, 
and acts as a colossal magnet — all little magnets anywhere on its 
surface setting themselves in obedience to its magnetic force, and 
turning their poles to point to its great magnetic poles, just as frag- 
ments of magnetized needles placed themselves on his earthkin, fash- 
ioned from a lodestone as a model of the earth. Gilbert thus de- 
stroyed the erroneous notion that the directive power of the compass 
needle was due to any cause outside the earth, and he fastened our 
tention in regarding its behavior, not on the attraction of a pole 
ir or a celestial pole, but on the magnetic qualities of the earth 
>elf. 

We must then turn to consider the facts in support of this con- 



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THE EARTH, A GREAT MAGNET 53 

ception, and first make reference to two historical discoveries, — one, 
that of Columbus, who discovered the " variation" of the needle; and 
the other, that of Hartmann and Norman, who discovered the " dip." 
In Columbus's first voyage to America, on the evening of Sep- 
tember 13, 1492, he noticed that the magnetic needle did not point 
exactly to the pole star, and that as he went westward this deviation 
increased. Up to that time no one had noted the fact that the 
needle did not everywhere point to the true North Pole ; but the 
voyage of discovery which revealed the new world, opened up also 
a fresh discovery in magnetism, and the variation of the needle from 
the true geographical meridian, or north and south line, became a 
recognized fact. Two other things also about it became later 
known, — one, that this variation is not the same at different places; 
and the other, that the variation itself varies at any one place. It 
appears that the first careful measurements of this variation were 
made in England by Burroughs, comptroller of the navy in the 
reign of Elizabeth. At that time in England the needle varied 
ii° 15' east of north. Since that date, the variation gradually 
changed in the manner shown in the following table : 





Mean variation of needle 


Date. 


Mean variation of needle 


ate. 


in London. 


in London. 


1580 


11° 15' E 


1787 


23 19' w 


1622 


60" 


1795 


23 57 " 


1634 


4 6 « 


1802 


24 6 " 


1657 


00" 


1805 


24' 8 " 


1665 


1 22 W 


1818 


24 34 " 


1672 


2 30 " 


1858 


21 54 " 


1692 


6 " 


1862 


21 23 " 


1723 


14 17 " 


1894 


17 23 " 


1748 


17 40 •• 


1895 


17 17 " 



The compass needle in England has in the last three hundred 
years, therefore, been very slowly changing its mean direction. 

In Queen Elizabeth's reign, it pointed eleven degrees east of 
north, or about one point east; in the days of the Commonwealth, it 
had returned to point due north. It then slowly marched westward, 
and three years after the battle of Waterloo, it reached in London its 
greatest westerly excursion of 24^ degrees west. Since that time 
it has been gradually diminishing again. In all other places there 
is a corresponding kind of secular change, as it is called, in the po- 
sition of the needle. Encircling the earth there is an irregular line, 
called the line of no variation, and all along that line (which is 
slowly changing its place) the compass needle is directed in a true 
north and south direction. This fact gives you your first glance at 
the truth that the earth's magnetism is not fixed, but is in a con- 

3 



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54 /• ^- FLEMING tvoi~ n, no. *} 

stant state of change ; and more, not only are there these great and 
slow changes of position in the needle at any one spot, but there 
are small daily and yearly movements of the needle, which are reg- 
ularly repeated, and also certain very irregular sudden motions, of 
which more shall be said presently. 

Then as regards the "dip" of the needle, Norman, in 1576, first 
announced, in a little book called the " New Attractive," the fact 
that if a steel needle, carefully balanced and free to move in a vertical 
plane, is magnetized, it dips downward by a certain angle called 
the 44 dip." 

At one spot in each hemisphere of the earth there is a place where- 
such a dipping needle stands vertically, and these places are called 
the earth's magnetic poles. These magnetic poles do not coincide 
with the true geographical poles. There is an irregular line round 
the earth on all points of which the needle sets itself horizontally, 
and this line is called the magnetic equator. This terrestrial " pole 
of verticity " was reached by Sir James Ross in his Arctic expedi- 
tion in 1831 ; and he found the dip needle pointed vertically to the 
earth's surface at a spot in the north of North America. Its posi- 
tion he determined to be latitude 70 5' 17" N„ and longitude 96 
45' 48" W. This locality agrees very well with a position deter- 
mined by calculation by the great mathematician Gauss. 

It only remains to be said that the " dip" at any place has its 
slow periodic, its daily and its yearly changes, like the variation. 

In the next place, I wish to point out to you that as a first ap- 
proximation, but only very roughly, we can imitate this magnetic 
condition of the earth by a model globe, having a short magnet 
stuck through its center, but with its axis oblique, or inclined, to 
the true polar axis ot the globe. If we construct such a model and 
carry round it to different places a small magnetic needle, we are 
able to show that there would be two places where the dip would 
be ninety degrees, and also that there would be a variation of the 
needle and a line of no variation. We may also imitate in a very 
rough way the changes of declination by supposing this internal 
magnet to revolve round, keeping its axis always at about the same 
inclination to the earth's polar axis. 

But the progress of knowledge soon showed that this rougb 
hypothesis is by no means sufficient to explain even approximately 
all the facts. 

Long ago it was felt that, as a first step towards better knowledge, 
a complete magnetic survey of the globe was an imperative necessity,. 



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THE EARTH, A GREAT MAGNET 55 

and also the establishment of magnetic observatories in various 
places to record the magnetic changes, and measure the magnetic 
elements. Accordingly, at Kew and at many other places, such 
magnetic observatories were established ; and in numerous expedi- 
tions, public and private, magnetic measurements have been made, 
at hundreds of places on the earth's surface, of the variation of the 
needle, the dip of the needle, and the earth's magnetic force or field, 
and the results have been embodied in magnetic charts. 

These charts exhibit the isogonic lines, or lines joining places of 
equal variation ; isoclinic lines, or lines joining places of equal dip ; 
and isodynamic lines, or lines joining places of equal magnetic 
force. The irregular distribution of magnetism, as shown by these 
charts, can not be reconciled with the supposition that the earth acts 
as a simple magnet. 

At magnetic observatories, such as Kew, the elements are con- 
stantly recorded by photography, and the movement of a spot of 
light, reflected from a mirror fixed to the magnet, is made to record 
on photographic paper a curve, showing the changes from moment 
to moment in the different elements. "On that paper the never- 
resting heart of the earth traces, in telegraphic symbols, the record 
of its pulsations, and also the slow but mighty working of the changes 
which warn us not to suppose that the inner history of our planet 
is ended." (Maxwell.) 

The diagram before you represents a part of such a two-days' 
diagram for the instruments at the Kew Magnetic Observatory, 
measuring the declination or variation and the earth's horizontal 
and vertical magnetic force. These photographic records, which 
have been kept at Kew for over a quarter of a century, show that, 
in addition to these slow, regular changes, the earth's magnetism 
is frequently in a state of more or less violent disturbances, and 
these disturbances are called magnetic storms. 

A magnetic storm may be going on when the sky is cloudless 
and air calm. Magnetic storms are intimately connected in some 
way, we know not yet how, w r ith changes on the sun's surface, pro- 
ducing sun-spots, and they always accompany displays of that elec- 
trical appearance called the aurora, so frequent in higher latitudes 
and especially so near the earth's magnetic poles. 

There is a close connection between all these phenomena. The 
years of most frequent sun-spots are separated from each other by a 
period of about eleven years, and the years of the greatest number 



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5 6 /• A. FLEMING [Vol ii, no. 2.1 

of magnetic storms and also of auroras appear to coincide with those 
years of the maximum number of sun-spots. 

Thus the year 1859 was a year of maximum number of sun-spots, 
and it was a year of great magnetic disturbances. Again, 1 870-1 871 
was remarkable as a year for numerous sun-spots and magnetic 
storms, and of frequent auroras, seen even as low down as London. 

Our modern investigations lead, therefore, to the conclusion that 
the earth is alive with ever-changing magnetic forces, and its mag- 
netic state at any point is not only altering in a slow progressive 
manner, like the solemn march of constellations in the heavens, but 
has its daily tides like the ocean, and also, like the restless sea, is 
ever and again thrilled with little ripples or waves of changing mag- 
netism, or lashed into a furious magnetic storm. 

These periods of magnetic storm coincide with times of great 
activity on the sun's surface, as evidenced by the presence of nu- 
merous sun-spots. 

The earth may therefore be described as a very irregularly 
magnetized magnet, with a pole magnetically similar to that which 
we call the south pole of a magnet somewhere on the north of 
North America, and an opposite pole somewhere in the Antarctic 
Ocean, but not at opposite ends of a diameter, and at some distances 
from the geographical poles. This great magnet is undergoing 
small, but fairly regular daily and yearly magnetic changes, and also 
sudden, irregular, and sometimes very great magnetic changes, called 
disturbances or storms. 

We have said that we can not explain the facts of the earth's 
magnetism merely on the supposition that it is a single magnet. 
One proof of this is that there are two places in the Northern Hem- 
isphere — one in the north of Canada, and the other in the north of 
Siberia — where the terrestrial magnetic force has a maximum value, 
and these are called the magnetic foci. 

Leading authorities have contended that we can not explain facts 

of the earth's magnetic condition without admitting that there are 

ft™ svstpms of magnetism superimposed, one having reference 

ger focus in Canada, and the other to the weaker in 

md since his time others, have endeavored to account 
secular changes of the declination by the revolution of 
focus round the globe, but the most recent discussion 
does not give support to this idea, but rather to the view 
anges are taking place at many points. 



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THE EARTH, A GREAT MAGNET 57 

Then arises another question. What is the cause of the earth's 
magnetism ? 

There are two ways in which we can produce a magnetic field, — 
one by means of permanently magnetized steel or iron, and the 
other by sending an electric current through a conducting circuit. 
Hence the earth's magnetic condition may arise either from the ma- 
terials of which it is made being permanently magnetized like lode- 
stone, or it may arise from electric currents circulating round the 
earth in its crust, or from both causes together. We know that 
there are such earth-currents, but we are at present unable to say 
whether the magnetic state of the earth has arisen as a consequence 
of these earth-currents or is merely influenced by them. 

If the magnetic state arises from a permanent magnetization of the 
materials of which the earth is made, then it must be wholly confined 
to the outer layer of the earth's crust, say within a depth of ten or 
twelve miles. We know that as we descend into the earth, the tem- 
perature rises at the rate of about i° Fahr. for each fifty feet of 
descent. An easy calculation, then, shows us that at a depth of about 
twelve miles the temperature would be about 1,200° Fahr., which is 
a bright red heat. At this temperature iron and lodestone and steel 
become quite non-magnetizable. A red-hot iron ball is not attracted 
by a magnet, and a magnet heated red-hot becomes demagnetized. 
The fact that a lodestone lost its magnetic power on heating in the 
fire was known to Fra Paolo and Porta in 1590. 

Hence it is quite clear that if the earth is magnetic in the sense in 
which a lodestone is magnetic, that it is not magnetic in the interior, 
but only on a relatively thin layer on the outside. For the earth is 
8,000 miles in diameter, and 12 miles is only sh of 4,000. 

Imagine a globe six inches in diameter representing the earth. 
We may take one-hundredth of an inch as the thickness of a sheet 
of writing paper. If such a globe was covered with writing paper, 
the thickness of that paper would represent to the same scale a 
depth of twelve miles. Hence we may say we live on the thin cool 
skin of a red-hot or white-hot globe, incandescent, but not fluid, in 
the interior. 

No permanently magnetized material can exist much below this 
thin skin or crust of about twelve miles thick. 

If, on the other hand, the magnetic powers of the earth are due 
to electric currents circulating in the mass of the earth, these may 
exist at much greater depths than twelve miles, because the very 
rise of temperature, which destroys permanent magnetism, probably 



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58 / A. FLEMING [Vol. ii, no. *.] 

renders the incandescent interior of the earth a much better electric 
•conductor than the cooler exterior rocks. 

Professors Riicker and Thorpe, in an elaborate magnetic survey 
of the British Islands, have come to the conclusion that many of the 
irregularities of the surface magnetic effects on the earth are to be 
attributed to the magnetic attraction of magnetized masses of rock 
below the surface, and since we know that the mean density of the 
earth is more than twice as great as the average density of rocks at 
the surface, it may well be that before we reach the limit below 
which permanent magnetism is impossible, there may exist a layer 
of earth crust in which iron compounds, or iron, form such a pre- 
dominant constituent that it possesses a high general magnetization, 
which, in consequence of changing temperature, is undergoing great 
magnetic changes. 

It would need almost a lecture in itself to give you an idea of 
the many different suppositions which have been made to account 
for the mode by which the earth became a magnet. Taken as a 
whole, it is a feeble magnet. 

If our globe were wholly made of steel, and magnetized as highly 
-as an ordinary steel-bar magnet, the magnetic forces at its surface 
would be at least a hundred times as great as they are now. That 
might be an advantage or a very great disadvantage. 

The remarkable fact about the earth's magnetic state is, that the 
two hemispheres, northern and southern, are magnetically different. 
In other words, there is a want of symmetry. Now the one great 
natural phenomenon with which it agrees in this respect is that of 
the earth's rotation, and there are many lines of thought which lead 
to the notion that the earth's magnetic state may have been origin- 
ally produced by, even if it is not maintained by, the earth's diurnal, 
or daily, rotation. 

Many are the hypotheses which have been put forward to ac- 
count for the close connection between sun-spots, auroras, magnetic 
storms, and earth's currents. One of the most ingenious of these is 
<iue to Sir George Stokes. 

Then, leaving speculations for which we have but slender ground, 
let me show you, in conclusion, some effects which the earth as a 
great magnet can produce, in which it acts just as do our smaller 
magnets in the workshop or laboratory. 

You have already seen that a piece of iron placed in the field of 
a magnet becomes itself magnetized. In like manner every piece of 
iron, which has stood long in a direction nearly coinciding with the 



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THE EARTH, A GREAT MAGNET 59 

earth's magnetic force, is magnetized. Hence, in England, where 
the dip is nearly 70 , all vertical bars of iron are magnetic. If you 
try with a little pocket-compass, you will find all iron pillars or long- 
iron pipes in a vertical position are magnets, and have a north pole 
at the lower end ; try, even with a pocket-compass, iron railings in 
front of a kitchen area, and you will find the same. This fact was 
known to Gilbert. 

Hammering a bar of iron, placed in the north and south position, 
facilitates the acquirement of this earth-produced magnetism ; and 
the magnetism so produced in the framework and shell of iron ships 
is a cause of great disturbance of the compasses in them, which 
requires correction. 

•Then, in the next place, a magnet can create an electric current 
in a coil of wire when it is moved to and from it. This was dis- 
covered by Faraday in 183 1. In like manner, turning or moving: 
a coil of wire over in front of the earth in such manner that a 
change is made in the apparent size of the coil, when looked at in 
the direction of the earth's magnetic force, will create an electric 
current in the coil. This is the principle underlying the dynamo- 
machine. Lastly, if a movable coil of wire has an electric cur- 
rent sent through it, when that coil is appropriately placed in front 
of a magnet, it will cause the coil to move, and we have here the 
fundamental principle of the electric motor. 

Mr. Swan has constructed and lent to me a coil of wire called a 
Gramme ring, which is so delicately poised that when a current of 
electricity is sent through the coil, it is caused to rotate by the mag- 
netism of the earth. We are using, in this experiment, the earth a& 
the field magnet of our motor. 

• Here, then, are three lines of proof which sustain the argument, 
which has been the subject of my discourse; viz., that the earth is 
a great magnet. 

No words are needed to enforce the enormous value of that fact 
in its intimate relation to the art of navigation. 

To us as a maritime nation, to you who are inhabitants of a mari- 
time city, the progress of a knowledge of terrestrial magnetism, the 
improvements in the compass, the study of the causes of error in 
iron ships, in short, everything connected with the use and evolution 
of the compass, is of unspeakable importance. Time has failed me 
to even mention the invaluable contributions of Lord Kelvin to this 
particular part of the subject. 

That great empire which has its center in these islands, but its. 



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60 / A. FLEMING [vol. ii, no. i.j 

dominions scattered over distant seas, has been built up primarily 
on the art of navigation, in which the magnetism of the earth is a 
central fact. Neither its world-wide commerce, nor the naval power 
which defends its coasts, could exist for a day without the aid of the 
magnetic compass. But our globe, as it spins through space, is 
clothed, as it were, in a gossamer garment woven of lines of mag- 
netic force, and this little trembling needle serves as a sensitive 
finger, whereby we track out the path of these invisible clues, and 
confidently determining our direction, though wandering over wide 
waters, wrapped, it may be, in darkness or in storm, are enabled 
thereby to establish a continual intercourse between all portions 
of the habitable globe. 



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THE ELECTRIFICATION OF THE ATMOSPHERE.' 
By Alexander McAdik. 

Will the twentieth century number among its triumphs a com- 
plete electrical survey of the atmosphere ? There are some good 
grounds for believing that it will. 

In the first place, the subject of atmospheric electricity, unlike 
the commercial problems in electricity, has not been attacked by 
an army of workers, swarming on each new phase and forcing 
further development by tireless industry and determined zeal. 
The appearance of three such papers as are referred to below in- 
dicates a quickening and wide-spread interest in the subject. 
Secondly, although we still lack a guiding theory as to the origin 
of the earth's negative charge, valuable data are accumulating so 
rapidly, and are now so accessible, that erroneous hypotheses may 
be quickly and effectively put to the test and disposed of. And 
thirdly, in the matter of instrumental equipment, we know the 
weakness of our present methods and apparatus, and also under- 
stand that where so many independent variables are to be dealt 
with, care must be taken to properly evaluate the electrometer 
readings. Furthermore, as with problems in meteorology, we must 
reach out from the individual observations to a series of similar 
simultaneous ones. The general laws of the potential variation in 
free air will be forthcoming when the necessary observations are 
made at many places. It is as logical for one to use a single ther- 
mometer to foretell marked temperature changes as to use a quad- 
rant electrometer, and hope to determine from a series of isolated 
readings much of value concerning the potential of the air. 

It is gratifying to note that in all recent investigations the ten- 
dency is to interpret observations rather than collect them. With- 
out disparaging the results of early workers, we insist upon work 
of a different order in future. It is now very well known that the 
exposure will largely control the values obtained. We have many 
tables of observations, but all with different exposures, and it is 

*" Observations on Atmospheric Electricity at the Kew Observatory." By C. 
Chree, Proc. Royal Soc. % vol. 60. 

"Review of Recent Investigations in Atmospheric Electricity." By J. Elster 
and H. Geitel. Extract from Part II of the Report of the Chicago Meteorological 
Congress, August, 1893, pp. 510-522. 

"Atmospheric Electricity." Lecture delivered before the Royal Institution of 
Great Britain, February 22, 1895, by Professor Arthur Schuster. 

4 61 



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62 



A. McADIE 



[Vol. II, No. a.] 



rather hard to reconcile the resulting mean values of the potential 
of the air. Enough of this kind of work has been done. 

The following table will give at a glance the work of the chief 
investigators from the time of Franklin to the end of the eight- 
eenth century. Passing Peter Collinson, of London, who intro- 
duced to the notice of the Royal Society the experiments of 
Franklin, and the three less known workers— J. H. Winkler, who 
wrote in 1746 on the electrical origin of the weather lights; Maffei, 
1747; and Barbaret, 1750 — we have: 



DATE. 


NAME. 


1751 


Franklin 


1751 


Mazeas 


1752 


Nollet 


1752 


Watson 


1752 


De Lor 




De Buffon 


1752 


IVAlibard 


1752 


Le Monnier 


1752 


De Romas 


1752 


Mvlius Ch. 


1752 


Kinnersley 


1752 


Ludolf and 




Mylius 


1753 


Richtnan 


1753 


Canton 


1753 


Beccaria, G. 




B. 


1754 


Lining 


x 753 


Wilson 


1755 


Le Roi 


1756 


Van Mus- 




schenbroek 


1759 


Hartmann 


1769 


Cotte 


1772 


Roynayne 


1772 


Henley 


1775 


Cavallo 


1784 


De Saussure 


1786-7 Mann 



REFERENCES. 
Phil. Trans., xlvii p. 289 
Phil. Trans., 1751, 1753 
Recher. sur les causes, 

1749-1754 
Phil. Trans., 1751, 1752 
Letter of Abbe Mazeas, dated 
St Germain, May 20, 1752 



1788 Volta 

1788 Crosse 

1 79 1 Read 

1792 Von Heller 
1792 Schiibler 



EXPERIMENTS. 

Effects of lightning 
Kite experiments 
Theory of electricity 

Electricity of clouds 

Iron pole 99 feet high, mounted on 

a cake of resin 2 feet square, 3 

inches thick, Estrapade, May 

18, 1752 
Sparks from thunder-clouds, 40 Mem. l'Acad. r. 

foot pole in garden at Marly; May, 1762 

also wooden pole 30 feet high, 

at Hotel de Noailles 
Observations of air charge 
Observations of air charge; kite 

experiments • 
Observations of air charge 
Observations of air charge 

Observations of air charge 

Electrical gnomon 

Electricity of clouds 

Systematic observations with an 

electroscope 
Kite experiment 
Experiments 
Experiments 
Kite experiments 

Origin of electricity 

Memoirs on Meteorology 

Fog observations 

Quadrant electrometer 

Fogs, snow, clouds, and rain ; kite 
experiments 

Observations 

Daily observations with an elec- 
trical machine, timing the rev- 
olutions to produce a given 
spark with a record of the 
weather 

New electroscope 

Experiments with collectors 

Insulation and conductors 

Observations 

Observations with weather rod 



des Sci., 



Mem. de Paris, 1752 

Mem. Sav. Etrange H, 1755 

8vo, Berlin, 1752 
Franklin's letters, 

Phil. Trans., 1763, 1773 
Letter to Watson 

Phil. Trans., 1753 
Phil. Trans., 1753 
Lett, del Elet, Bologna, 1758 

Letter to Chas. Pinckney 
Phil. Trans., 1753, P- 347 
Mem. de Paris, 1755 
Intro, ad Phil. Nat, 1762 



Journ. Phys., xxiii, 1783 
Phil. Trans., 1772 
PhiL Trans., 1772 
Treatise on Elec, 1777 

Voyage dans les Alps 



Lettere sulla Meteor, 1783 
Gelb. Ann. Bd., 41 
Phil. Trans., 1791 
Green's Jour. d. Phys. 2 Bd.,4 
J. de Phys., lxxxiii 



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ELECTRIFICATION OF THE ATMOSPHERE 63 

At the beginning of the nineteenth century, Schubler, at Tubin- 
gen, systematically observed for twenty years and worked out a 
curve of diurnal variation. Double maxima and minima were de- 
termined; the first maximum about 8 a. m., and the second about 
8 p. m. The minima occurred before sunrise and about sunset. 
Correlating the values with weather conditions, Schubler found in 
no cases of rain, 63 negative values and 47 positive ones; while in 
33 cases of snow, 27 were positive and 6 negative. 

Peltier's modification of the electroscope and his views on the 
origin of atmospheric electricity led to a series of observations by 
A. Quetelet, beginning in August, 1842, at the Observatory at Brus- 
sels. After some improvements in the electroscope were made, 
another set of observations was made in 1844, and it appeared that 
no negative values were observed except during rain. Indeed, 
negative values were rare, only 23 cases being recorded in four 
years. Passing the observations made at Dublin by Clarke in 
1839, we come to those made at the Observatory at Munich by 
Lamont, in 1850-51, with a Peltier electrometer and methods about 
the same as at Brussels. The monthly and annual means are given 
in PoggendorfPs Annalen, lxxxv, 1852, pp. 494-504, and lxxxix, pp. 
258, et seq. In general, the winter months show a value nearly 
twice that of the summer months. About the same time, observa- 
tions were made at Kreuznach by Dellmann. The yearly values 
nearly agree, but the mean monthly values differ considerably. A 
minimum occurs in May and a maximum in December. The air 
was generally positively electrified. Smoke and fog gave high 
positive values, and dust caused a change from positive to negative 
for several hours and to a degree exceeding the positive. Rain 
gave sometimes high positive and sometimes high negative, the 
latter often when the rain had just ended. Snow almost always 
gave high positive. 

. Everett, at Windsor, N. S., made observations, generally three 
per day, and the results of these and later observations have been 
widely published, and are too well known for extended notice now. 
During the same time, Wislizenus, at St. Louis, Missouri, made ob- 
servations, and has given the annual and diurnal curves of these. 
Two maxima and two minima are shown in the diurnal curve and 
a maximum in winter. In all, Wislizenus made some 25,000 ob- 
servations, and his conclusions are therefore of more weight than 
those of any other observer up to that time. The normal state of 
the air is positive, and negative is an exceptional and temporary 



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64 A McADIE [vol. n, no. 2] 

condition. Marked disturbances were experienced at times of 
thunder storms. Fog was occasionally accompanied by negative 
indications, but alter fine drizzling rain, fog as a rule was accom- 
panied by positive values, often very high. A full discussion of 
the . observations may be found in the American Meteorological 
Journal for 1887. 

We have not space to do more than simply mention most of 
the other observers. W. A. Birt has given an elaborate discussion 
of the Kew Observations of 1845-6-7 in the Report of the British 
Association, 1849, p. 113. At Gaud, Duprez studied the observa- 
tions made from 1855 to 1864, and brings out particularly the re- 
lation to cloudiness. Palmieri at Vesuvius, in 1850, and later with 
simultaneous observations at Naples and Vesuvius, found that the 
potential was lower at the higher station. In this conclusion he is 
at variance with all other observers. Some observations that are 
worthy of notice were made with a water-dropper collector at Per- 
nambuco, from October, 1876, to February, 1877. On the rare 
occasions in which a negative potential was recorded, there were 
heavy rains and more or less cloudiness. We now come to the 
very important observations made at Paris by Mascart and others 
under his direction. The apparatus was installed at the College de 
France in February, 1879, and continuous records covering some 
years were obtained. In general, the potential of the air was posi- 
tive. Rain was almost always accompanied by large negative 
values. The change in character occurs previous to the rain, and 
sometimes the rain is followed immediately by high positive values. 
A very full discussion of the observations made by the United States 
Signal Service is given in the Memoir of the National Academy of 
Sciences, by Professor T. C. Mendenhall. It is to be regretted that 
this discussion is not more generally known ; for there are many 
valuable suggestions in it, concerning mechanical collectors, best 
forms of electrometers, proper exposures, and details of methods to 
be followed, of great benefit to those who are to take observations. 
There is also an elaborate discussion of the question, " In the pres- 
ent state of meteorological science, can the observations of atmos- 
pheric electricity be utilized in forecasting the weather?" A very 
thorough set of observations was made by Mtiller and Leyst, in 
Russia, with a Carpentier form of Mascart Electrometer. The 
mean values for bi-hourly observations made at Pawlowsk in 1884 
are given in Annalen des Phys. Cent. 06s. t Part I, 1884. Other ob- 
servations are those made by C. Michie Smith, in Madras, in 1883 



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ELECTRIFICATION OF THE ATMOSPHERE 65 

and 1884; Abercromby, at the Peak on the Island of Teneriffe; 
Dr. Fines, at Perpignan, with photographic apparatus of the Mas- 
cart pattern, and continued for a number of years. Roiti, Magrini, 
and Pasquilini have two years' complete records at Florence. Ex- 
ner's extensive experiments on the potential gradient, Andree's 
observations near the pole while on the Swedish Expedition, and 
the work on the Sonnblick by Elster and Geitel, bring us down to 
the present state of the problem. 

The recent Kew experiments were undertaken to verify Exner's 
law that a building reduces the potential of the air, precisely as if 
it formed an integral part of the earth's surface. A portable elec- 
trometer was carried to five stations near the Observatory, and the 
mean values of the several ratios found to be approximately con- 
stant. The meteorological elements are then discussed, and partic- 
ularly the moisture, to see whether the potential gradient is so 
closely connected with the aqueous vapor as Exner claims. The 
results do not support the theory. The influence of bright sun- 
shine in reducing the potential gradient, as shown by Elster and 
Geitel, seems more likely. The potential was lower after long sun- 
shine. The evidence " in favor of a connection of high potential 
with low temperature is just about as strong as that in favor of a 
connection of high potential with little previous sunshine." 
Higher potential was found to be associated with higher pressure 
in the forenoon observations, but to a less marked degree in the 
afternoon observations. Adopting eleven miles as a limiting value 
of the wind velocity, it was found that with a mean velocity of 19.6 
miles per hour, there was a mean potential of 153; and with a 
mean velocity of 6.8, the mean potential was 175. The author 
does not seem to be aware of the observations made in the United 
States upon similar lines. An attempt was also made to investi- 
gate the relation of the potential to cyclonic and anti-cyclonic 
weather. In five cases out of the seven considered, the mean po- 
tential for the anti-cyclonic condition exceeded that for the cyclonic. 
In Dr. Chree's words, " There is something to be said for the hy- 
pothesis: but individual occurrences of high potential in cyclonic 
weather and of low potential in anti-cyclonic weather were not in- 
frequent." 

The paper of J. Elster and H. Geitel is a most comprehensive 
review of recent investigations in the subject. For painstaking 
and systematic study of the potential as influenced by water vapor, 
sunlight, dust, and height, it cannot be excelled. 



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66 A. McADIE Lvol. ii, no. 2 j 

The views of von Bezold and Arrhenius concerning a photo- 
electric action of the solar radiation have been in part confirmed by 
these investigators. It has been experimentally shown that the 
sun's rays act on certain substances in such a way as to cause a 
loss of negative electricity. Our authors make the potential gra- 
dient vary with exposure to ultraviolet light. The marked disturb- 
ances occurring with precipitation are considered as disturbances of 
the normal field. They also think that Palmieri is right in his 
statement that whenever negative electricity is observed, rain falls 
close by. Sohncke and Luvini have shown how dry ice crystals 
were positively electrified through friction with dust-formed water, 
and Maclean and Goto, and more recently Lenard and Kelvin, have 
discussed the question of electrification through falling water. 
"When waterdrops strike on a fixed moist substratum or a larger 
water surface, the surrounding air at the time of impact shows 
itself as negatively electrified." And our authors think, with 
Lenard, that it is very probable that the negative values so preva- 
lent during rainy weather are in part due to this. With the build- 
ing of mountain observatories, the electric phenomena of the air, 
and more especially the silent discharges, come more readily under 
our observation. Elster and Geitel themselves have collected a 
number of observations relating to the appearance of St. Elmo's 
fire on the Sonnblick. It would seem that the phenomena are 
closely connected with climatic conditions and are to be studied in 
their development precisely as thunderstorms. 

Elster and Geitel have rendered a great service to future stu- 
dents of atmospheric electricity, by clearly pointing out the differ- 
ence between the normal field or fair-weather electricity and the 
accidental field, if it may be so called, when the electrical measure- 
ments are greatly influenced by dust, snow, clouds, precipitation, 
whirling air or smoke, spattering water, etc. " Certainly it is an 
improvement," they say, " to diminish the influence of the lower 
dusty strata of air through the employment of kites, as introduced 
by McAdie at Blue Hill, and later by Weber at Kiel, though it is 
questionable if the advantage is not too dearly bought by the impos- 
sibility of determining the height." Marked improvements have 
been made in kite methods since these words were written. Another 
important matter, touched upon by our authors, is the circulation 
of electricity from the earth into the atmosphere, and back again to 
earth. Theories are not wanting, but experimental determinations 
are. It is not improbable that a link in the chain of processes may 



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ELECTRIFICATION OF THE ATMOSPHERE 67 

be the aurora, and investigations in this direction are therefore 
greatly desired. Through such will the relation between the elec- 
tric and magnetic fields be brought out. This is, in our opinion, 
the coming question, "How are the magnetic elements and the elec- 
trical currents of the air r elated f" 

Professor Schuster's lecture is a most interesting risume* of the 
experimentation of Franklin's time with the modern lecture appa- 
ratus for studing the conduction of gases. The question of the 
breaking down of the air as an insulating medium is touched upon, 
and the effect of light and of the discharge itself considered. 
Electric sparks are liable to succeed each other along the same 
path, and Schuster thinks this points to a higher conductivity of 
the air along the path of the previous discharge. Schuster also 
thinks that the location of the positive charge, corresponding to 
the earth's negative charge, can only be ascertained through the 
agency of balloon and kite experiments. " Observations made up 
to heights of about 1,000 feet seem to indicate a strengthening of 
the electric field— i.e., the fall of potential per meter is greater at 
a height of, say, 200 meters than on the surface of the earth." 
The observations of Dr. Leonhard Weber and Dr. Baschin are re- 
ferred to — the former as showing how the fall of potential at a 
height of 350 meters was six times that at the earth's level; and 
the latter showing that at a height of 3,000 meters no fall could 
be determined, while at 760, 2,400, and 2,800 meters respectively, 
the fall in volts per meter was 49, 28, and 13 respectively. It 
seems therefore likely that the lines of force of the normal elec- 
tric field of the earth end within the first 10,000 or 15,000 feet. 
Schuster advances the somewhat startling view that the semi- 
diurnal variation of atmospheric electricity is connected with " the 
same circulation in the upper regions of the atmosphere which 
shows itself in the corresponding changes in pressure." He re- 

fers to Exner's formula: P = , , where A = 1300, k = 13.1, 

/ ~r * p.. 

p. — pressure of aqueous vapor present, in centimeters, and P= the 
electric force; and notes the agreement between vapor pressures 0.23 
and 0.95. It is the amount of vapor, and not the humidity, which con- 
trols. Elster and Geitel's ultraviolet radiation relation to electrifica- 
tion and amount of aqueous vapor present is also alluded to. 



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SECULAR VARIATION EXPRESSIONS OF THE 

MAGNETIC INCLINATION. 

By G. W. Litti.ehai.es. 

These expressions for the secular variation of the magnetic in- 
clination at various important maritime stations have been deduced 
with a view of providing for the computation of the rate of change 
at a station at any time within the period of observation, and of 
bringing forward, from one epoch to another, values of the inclina- 
tion observed in the regions were the stations are situated. 

They have been used in this manner in connection with the 
preparation of the chart of the world, lately published by the 
Hydrographic Office, showing the isoclinic lines for the epoch 1897. 

Taken in connection with the secular variation expressions of 
the magnetic declination, communicated by me to the Editor, and 
published in Vol. I, No. 2, the expressions for the inclination now 
presented furnish the means for investigating the secular change 
in the direction of a freely suspended magnetic needle at each of 
the twenty-two stations, in addition to those of Callao, Valparaiso* 
Hongkong, and Sydney, for which I have already furnished results. 
68 



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Arica 

Ascension Island 

Bahia 

Batavia 

Bombay 

Callao 

Cape of Good Hope 

City of Mexico 

Concepcion 

Coquimbo 

Kayal, Azores 

Habana 

Hongkong 

Honolulu' 

Magdalena Bay 8 

Manila 

Montevideo 

Panama 

Payta 

Pernambuco * 

Petropaulowski 

Punta Arenas 

Rio de Janeiro* 

St Helena 

Shanghai* 

Singapore 

Sydney 

Tahiti 

Valparaiso 


5* 

s 


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jo L. A. BAUER [vol. ii, no. a.] 

A REMARKABLE LAW. 

By L. A. Bauer. 

Let </ = tbe mean value for the year of the total diurnal range or ampli- 
tude of the magnetic declination, t = the diurnal range of the inclination /, 
^ = magnetic latitude, then will the following formulae give close approxima- 
tions to d and i for any place where 1 is known : — 

d = k sec** = 2 1 .58 sec*^ (f) 

% = #/ (i+3 s»n f *) =6 , .i/ (H-3 sin 1 *) (2) 

In proof of this see diagrams opposite. is obtained from the well- 
knowu formula, tau 7=2 tau ^. The test of the formulae is a severe one ; for 
k was derived from but 12 stations — all of them in the northern hemisphere — 
while in the diagram 12 additional stations (of which about half are from the 
southern hemisphere) are represented. k x was determined from only two sta- 
tions, Dublin and Batavia, while in the diagram the comparison is made for 
stations far distant from D and B. The only marked departures for (2) are 
shown by Tan Mayen and St. Helena. It should be recalled that i is far more 
difficult of experimental determination than d. The constants will be re com- 
puted for different years in the sun-spot cycle and for different seasons of the 
year. For this reason a tabular presentation is postponed.] (1) was found em- 
pirically and then deduced theoretically, thus: Let dH represent the com- 
ponent of the horizontal diurnal deflecting force at right angles to the mean 
direction of the horizontal needle, then is: tau % d = dff / H. Assume that 
dH varies inversely as //, and substitute for H the approximate value, 1 ) 
0.330 cos 0. Similarly we get (2) if we substitute instead ot H the total force, 
/^ = 0.330 |/ 1 -+- 3 sin*^? It would have been very difficult to find (2) empiri- 
cally. 

It will be seen from the formulae that d increases, while i decreases witH 
magnetic inclination (latitude). Precisely similar laws ! ) I deduced empirically 
two years ago with regard to the secular variation and the distribution of the 
earth's magnetism ; but, at the time, I did not perceive their mathematical 
formulation. I now have found the proper functions. Before I show this, it 
should be remarked that if (1) and (2) are correct, then the isoclinics represent 
closely the lines of equal diurnal range. 

Let d = the average secular range in the declination for a given geograph- 
ical parallel of latitude during the interval 1780— 1885, and similarly let 1 = 
the inclination range, then the following formulae will hold : 

<* = 3 -73s*c*^ (3) 

'=4 .57/(i + 3sin"« (4) 

See graphical comparison opposite. 

Finally, let [\ D = the difference in the extreme values of the declination 
along a geographical parallel of latitude at any given period. [I have termed 
l_\D the "longitudinal range;" but " distribution range" would perhaps be 
better.] Similarly let A / = the inclination difference ; then we -have : 

tau i'\D = 0.256 sec 1 ^ (5) 

tau A /= 0.535 / (1 + 3 sin 2 $) (6) 

The diagrams opposite prove the validity of these formulae. The quanti- 
ties [\D and i\I are the average values') for the interval 1780-1885. ^ was 
obtained from the mean inclination for the given parallel. It may in this 
case be taken as practically equal to the geographical latitude. ') Nos. 3, 4, 
5, and 6 can be obtained theoretically in the same manner as (1) and (2). 
The law assumed in each case is that the component of the deflecting force 
producing the angular deflection of the needle Jrom its mean position is in- 

MSee my papers entitled, " On the Distribution and the Secular Variation of the 
Earth's Magnetism." Nos. I and II, Am. Jour, of Science, Vol. I, pp. 109-115, and 

189-204. 



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A REMARKABLE LAW 



71 



versely proportional to the force exerted on the needle by the earth's per- 
manent magnetism. Does a similar law hold for the disturbances ? 

With the aid of these formulae we find that diurnal deflecting force ; aver- 
age annual amount of the secular deflecting force ; distribution deflecting 
force (the force for example which causes the compass to depart from a true 
north and south direction), for the declination, as 1:0.83:682, and for the 

inclination, as 1 : 0.86 : 604, 
d/f= 0.0000409 / //, and dF= 0.0000965 / F. 




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LETTERS TO EDITOR 



S. STEVIN'S AIMENEYPETtKH. 

Seitdem ich Ihnen die in Terrestrial Magnetism I, 153 abgedruckte 
Mitteilung iiber dieses Buch machte, habe ich etwas Genaueres iiber das- 
selbe in Erfahrung bringen konnen. 

Zunachst mochte ich feststellen, dass das hollandische Original wirk- 
lich 1599 erschien und nicht 1586, wie Ch. Frisch annahm (Kepleri Opera 
omnia III, 457), und nach ihm 6". Gunther (J. Kepler und der tellurisch- 
kosmische Magnetismus, S. 41), wahrend W. van Bemmelen (De Isogonen 
in de XVI de en XVII de Eeuw, S. 5) 1596 fur wahrscheinlicher halt. Ich 
habe namlich Gelegenheit gehabt, auf der koniglichen Bibliothek im 
Haag ein Exemplar des ausserst seltenen Originaldruckes einzusehen. 
Derselbe fuhrt folgenden Titel : 

DE I HAVEN- I VINDING | [Holzschnitt mit dem "Garten von Holland," 
in der Mitte die Magd] I Tot Leyden, I In De Drvckerye van 
P^antin, I By Christofpei* van Ravelenghien, I Gefworen drucker 
der Univerfiteyt tot Leyden. | cId . Id . ic . | 9ttet sprtiitlejjte. | 

Das Buch enthalt nur 28 gez. Quart-Seiten. Das Verzeichnis der De- 
clinationen, vermutlich das alteste seiner Art, steht auf Seite 10 und 11. 

Ferner habe ich neulich auf der Pariser Auction einer wertvollen 
Sammlung Plantinscher Drucke ein Exemplar der gleichfalls seltenen 
lateinischen Ausgabe erwerben konnen, die ich auch inhaltlich etwas 
genauer beschreiben will. Der Titel lautet : 

AIMENETPETIKH, | five, | PORTWM | INVESTIGANDORVM | RATIO. | 
Metaphraste Hug. Grotto Batavo, I [Drucke rsignet von Plan tin] | Ex 
Officina PtantinianaX Apvd Christophorvm Raphelengivm, I Academiae 
Lugduno-Batauae Typographum. clD . Id . IC . 

Das Format ist dasselbe Klein-Quart, wie beim hollandischen Origi- 
nal; der Umfang 6 unbez. Blatter und 21 bez. Seiten. 

Die acht Seiten beanspruchende Einleitung tragt die Ueberschrift : 
"Duci, Senatui, Populoque Veneto ,, und ist vom Uebersetzer Hugo de 
Groot gezeichnet. Aus ihr erf ahrt man, dass Graf Moritz von Nassau, 
von Oranien, als Admiral der hollandischen Flotte den Mathema- 
Simon Stevin zur Abfassung der Schrift veranlasst hat, weil er von 
ichtigkeit der Kenntnis der magnetischen Declination fur den See- 
iiberzeugt war. Auf des Prinzen Geheiss erschien das kleine Buch 
12 



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LETTERS TO EDITOR 73 

gleichzeitig in mehreren Sprachen (hollandisch, lateinisch, englisch und 
franzosisch), um in Seemannskreisen grosse Verbreitung zu finden. Der 
lateinische Uebersetzer de Groot wendet sich auch in der Einleitung an 
die Venetian ischen Seeleute mit der Bitte, fleissig Declinations-Beobach- 
tnngen zu machen. 

Der eigentliche Inhalt der Schrift besteht in einer Auseinandersetz- 
ung der Bedeutung der magnetischen Declination fur die Schifftahrt, in 
einer Liste der Werte der Declination von 42 Orten der Erde und in 
einer Anleitung zur Beobachtung derselben mit Hilfe eines Azimuthal- 
Compasses. Als Gewahrsmann fur die Declinations- A nga ben wird aus- 
driicklich der "doctissimus Geographus P. Plancius" genannt. Dieser 
in Amsterdam lebende calvinistische Prediger hatte die Angaben fur 
eine anscheinend verloren gegangene geographische Karte gesammelt, 
die er 1592 vollendet haben soil. Daraus ergiebt sich wohl ohne weite- 
res, dass sich die Declinationswerte durchaus nicht auf dieselbe Epoche 
beziehen, sondern sehr verschiedenen, zum Teil weit auseinanderliegen- 
den Zeiten entsprechen. So stitnmt z. B. die Angabe der Declination fur 
Ooa in Ostindien 15 io' E fast genau mit dem Werte iiberein, den Joao 
de Castro 1538 gefunden hatte, namlich 15 E. Eine Verwertung dieser 
Plancius-Stevinschen Tabelle der Declinationen fur die Ableitung der 
Sacular- Variation ist daher kaum moglich. 

Die Grotiussche lateinische Uebersetzung ist auch sprachlich interes- 
sant, weil sie zum ersten Male einige technische Ausdriicke benutzt, die 
sich bei spateren lateinisch schreibenden Schriftstellern iiber den Mag- 
netismus, wie Kit c her, Cabeo y Scarella, Leotaud u. A., genau so wieder- 
finden, z. B. declinatio, chalyboclisis, anatolismus, u. s. w. 

Berlin, im Marz 1897. G. Hellmann. 



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74 W. VAN BEMMELEN [vox., n, No. a .j 

"the non-cyclic effect" und "die erdmagnetische 

nachstorung." 

Da ich meine, dass ein Referat nur wenig die Grenzen einer Inhalts- 
besprechung iiberschreiten darf, will ich die Arbeit des Herrn Chree im 
Zusammen hang mit meinen Resultaten hiergesondert behandeln. Im Jahre 
1 895 erschienen unsere Schriften fast gleichzeitig und ganzlich unabhangig 
von einander. 1 Da Herr Chree diese Sache weiter verfolgt und meine 
Arbeit nur mit einigen Zeilen oberflachlich beriihrt hat, Herr Ellis in 
seinem " Appendix " meine Untersuchungen nicht erwahnt, kommt mir 
eine nahere Besprechung in dieser Hinsicht nicht uberfliissig vor. 

Das Material des Herrn Chree leidet an dem Uebel, dass es nicht in 
steter Uebereinstimmung mit dem Forschungs-Ziele und den -Resultaten 
gewahlt wurde, sondern dass es ein im Voraus gegebenes war. Wozu 
dienen denn die umstandlichen Publicationen der magnetischen Obser- 
vatorien, wenn man sich nur an die teilweise bearbeiteten Beobachtungen 
seines eigenen Observatoriunis halt ? 

Fur den Einfluss auf das Jahresmittel hat Herr Chree auch schon zu 
den Pawlowsker Beobachtungen seine Zuflucht genommen. Wiewohl 
der Ausgangspunkt meiner Arbeit ein anderer gewesen ist, da ich zuerst 
die, einer Stoning folgende, ruhige Periode untersuchte, sind doch die 
Normaltage gesondert von mir verarbeitet worden. Ich habe immer 
zwei aufeinander folgende Normaltage beniitzt und die Unterschiede der 
Tagesmittel berechnet, wahrend Herr Chree die Unterschiede zwischen 
den Mitternachts-Werten nimmt. Seinen Werten des " non-cyclic Effects " 
klebt somit der Einfluss einer etwaigen tiiglichen Schwankung an, und sie 
stiitzen sich ausserdem auf eine 24mal geringere Zahl von Beobachtungen. 
Weiter sind die von mir beniitzten Normaltage Pawlowsks frei und nicht 
mit dem Zwange einer bestimmten Anzahl pro Monat gewahlt, wahrend 
die Beobachtungen bekanntlich hochst genau sind.. 

Jedoch habe ich mich nicht auf die Tagesmittel beschrankt, sondern, 
gleich wie Herr Chree, die Unterschiede fur correspondierende Stunden- 
werte untersucht. Dies aber nicht fiir eine Station und eine Stunde, 
sondern fur die geographisch sehr verschieden liegenden Stationen Paw- 
lowsk, Tiflis, Batavia und Kap Horn und fur alle 24 Stunden. Die Resul- 
tate sind nicht in Ziffern, sondern graphisch dargestellt worden. 

Zur weiteren Vergleichung habe ich mir die Rechenarbeit gefallen 
"ise tagliche Schwankung des "non-cyclic Effects" auch fiir 
der ruhigen Periode, welche einer Stoning folgt, abzuleiten, 
fiir die Stationen Kap Thordsen (Spitzbergen), Jan Mayen, 
md Pawlowsk (Sommer und Winter fiir Pawlowsk geschieden). 
hen Resultate, welche diese Arbeit geliefert hat, will ich hier 
der mitteilen, nur herv-orheben, wie sich aus den Figuren 
\ Assoc., Ipswich Meeting, 1S95; Meteorol. Zeitschr. XII, S. 321, 1895. 



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LETTERS TO EDITOR 



75 



herausstellt, dass die Mitternachtsstunde nicht die gliicklichste zur Be- 
rechnung des " non-cyclic Effects" ist. Die dazu passende Stunde andert 
sich mit der geographischen Lage. 

Herr Chree stellt in Tabellen zusammen die Anzahlen der Falle, in 
welchen sich der " non-cyclic Effect " positiv, null, oder negativ gezeigt 
hat, und die Grdssen in den verschiedenen Monaten, Quartalen und 
Jahren ; wobei es sich dann zuerst herausstellt, wie das Zeichen nur bei 
H und / constant ist. 

Die Resultate, welche ich bei den 28 von mir untersuchten Stationen 
bekommen habe, machen diesen Gegensatz erklarlich. Wenn man doch 
die Declination und Horizontal-Intensitat zu einem Horizontal- Vector 
vereinigt, stellt es sich heraus, wie das Azimut des Nachstorungs- Vectors 
eine constante und sehr typische Grosse ist. Sehr typisch, weil sie ge- 
stattete, die Nachstorungs-Meridiane iiber die nordliche Halbkugel zu 
ziehen und den Verband mit den Nordlicht-Linien (Isochasmen) darzu- 
thun. 

Dieses Azimut weicht meist vom magnetischen ab, ist aber in Green- 
wich zufalligerweise fast jenem gleich ; also sind die fur die Declination 
gefundenen Zahlen fur einen grossen Teil als Unregelmassigkeiten zu 
betrachten. Fur Pawlowsk, wo das Azimut i8 D war, liefert die Decli- 
nation immer Abweichungen im selben Sinne. Weiter bin ich, als ich 
die Petersburger Zahlen nach Semestern und Trim ester n einteilte, zu 
gleichen Resultaten, als Herr Chree, in Hinsicht auf die jahrliche 
Schwankung gekommen. 

Herr Chree schreibt: "As the title he selected implies, Dr. van Bem- 
melen associates the phenomena very intimately with magnetic storms. 
His investigations have included data from a variety of stations ; and 
whilst his theoretical conclusions may, perhaps, undergo a modification 
in the future," etc. 

Ich glaube, dass eine Kraft, welche fast immer unmittelbar nach den 
Storungstagen auftritt, welche in Grosse, vom Storungstag abgerechnet, 
geometrisch abnimmt, wie ich aus dem " General-Mittel " aller 28 Sta- 
tionen nachgewiesen habe, als verwandt mit diesen Storungen angesehen 
werden darf. Welche diese Verwandtschaft ist, dariiber habe ich mich 
gar nicht ausgelassen. Dass auch das Phanomen, welches wahrend den 
Normaltagen stattfindet, dasselbe ist, macht die vollige Uebereinstim- 
mung des Azimuts und des taglichen Ganges sehr wahrscheinlich. 

Herr Ellis sagt, dass die mit einem plotzlichen Stosse anfangenden 
Storungen dariiber vielleicht Auskunft geben konnen ; sagt aber nicht, 
dass ich bereits 12 solche Falle (nach den Utrechtern Magnetogrammen 
beurteiit) fur Greenwich untersucht habe, und dass es sich dabei heraus- 
gestellt hat, wie die Bewegung wahrend neun vorangehenden Tagen die 
gleiche, wie nach der Storung, war, aber gerade wahrend den letzten 
drei Tagen am wenigsten typisch. Nur die sich sonst so unregelmassig 
verhaltende Vertical-Intensitat zeigt eine regelmassige Abnahme. 



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7 6 W. VAN BEMMELEN [Vol. ll, No. a.) 

Ich denke mir die Sache so, dass die Kraft immer da ist, aber bei 
jeder Storung einen Impuls bekommt. Es wird doch wohl schwer sein, 
meine Aeusserungen in dieser Richtung "theoretical conclusions'* zu 
nennen ; auch anderswo habe ich immer nur Rechen- oder Beobachtungs- 
resultate neben einander gestellt und Theorien fern gehalten ; wenigstens 
keine theoretischen Schliisse gezogen. 

Ich hoffe, in diesen wenigen Zeilen klar gemacht zn haben, warum 
ich glaubte, dass es notig sei, angesichts der fliichtigen Beriihning mei- 
ner Arbeit durch Herrn Chree, hier die Resultate beider Abhandlungen 
kurz zu besprechen. W. van Bemmelen. 

Utrecht. 

RESULTS OF MAGNETIC OBSERVATIONS ON THE RIGI, 

MADE IN 1895 AND '96. 

In the spring of 1896 we completed, as we thought at the moment, the 
magnetic observations on and near the Rigi, commenced in 1895 with 
the intention of determining the influence which the altitude above sea 
level might have on the magnetic elements. After a careful discussion 
of the results, we came to the conclusion that our observations show 
that, as far as the Rigi is concerned, the horizontal component decreases 
slightly with the altitude, while the vertical one increases in a somewhat 
larger degree. This increase, however, seems not to be larger than about 
0.000 20 (C. G. S.) for 1 kilometer. These quantities are very small, if 
one bears in mind what the unavoidable errors of observation are. 

Moreover, although we were certainly confirmed in the conviction we 
already had from the work done in 1895, that the Rigi, as a mass, is not 
magnetic, our 1896 observations show that there are some faint lines of 
attraction. Under these circumstances we are inclined to believe that 
our results are not established firmly enough, and intend to attack the 
problem this spring in a different way. van Rijckevorsel. 

Rotterdam and Utrecht, April, 1897. Van BEMMELEN. 



THE MAGNETIC SURVEY OF MARYLAND. 

The detailed magnetic survey of this state, begun last year, has been 
resumed this summer, the Editor remaining in charge. An account of 
some of the results obtained thus far will be given in a future number 
of the Journal. Special stress will be laid this year upon the investiga- 
tion of the marked local or regional disturbances in Central and North- 
eastern Maryland, revealed by last year's work. There are prospects 
that a neighboring state will undertake a similar survey in the near 
future. 



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ABSTRACTS AND REVIEWS 



Chree, C. Non-cyclic Effects at Kew Observatory during the selected "Quiet " 
Days of the Six Years, 1890-95. Report of the Committee on Comparison 
and Reduction of Magnetic Observations, British Association, Liverpool 
Meeting, 1896. 

In dieser Abhandlung tritt der Verfasser dem Phanomene, welches er 
" non-cyclic Effect " nennt und welches er schon im vorigen Report (Ipswich 
Meeting, 1895, cf. diese Zeitschrift 1896, p. 95) hervorgehobeu hat, naher. Da- 
xnals hatte Verfasser die ruhigen Tage der Jahre 1890-94 beniitzt, und jetzt 
jene des Jahres 1895 mit in Betracht gezogen, indessen fiir die sechs Jahre 
auch, ungeachtet der Unsicherheit der Temperatur-Correction, die Vertical- 
Intensitat und Inclination bearbeitet. 

Als " non-cyclic Effect " wird wieder der Unterschied zwischen dem einem 
Tag vorangehenden und denselben schliessenden Mitternachts-Wert beniitzt. 
Da fiir jeden Monat fiinf ruhige Tage ausgewahlt sind, beruht der Mittelwert 
jedes einzelnen Monates auf fiinf Werten jenes Unterschieds. 

Die Resultate fiir Monate, Quartale und Jahre sind in Tabellen zusammen- 
gestellt und zur Vergleichung auch die Anzahlen ruhiger Tage angegeben, 
welche zusammen einen •• non cyclic Effect," welcher der Sacular- Variation 
pro Jahr gleich ist, liefern. Aus den Tabellen ist ersichtlich, dass allein die 
Horizon tal-Inten si tat und Inclination, und nicht die Declination und Vertical- 
Intensitat einen Effect mit bestimmtem Zeichen liefern. Zur Erforschung des 
Einflusses auf die Jahres werte der verschiedenen Elemente fehlten fiir die 
Kew'schen Beobachtungen die notigen Data und werden die Resultate von 
Miiller fiir Pawlowsk beniitzt. Es stellte sich heraus, dass das Jahresmittel 
nach alien Tagen und nur nach Normal-Tagen einen Unterschied mit con- 
stantem Zeichen hatte. 

Das Verhaltnis zu der taglichen Schwankung wird weiter besprochen und 
die Quotiente non-cyclic Effect | uncorrected range gege ben, wobei es sich 
herausstellt, wie der non-cyclic Effect besonders in den Wintermonaten eiuen 
bedeutenden Einfluss hat. 

Die moglichen Eliminationen des Effectes werden auch angegeben. 

In einer kurzen Besprechung einer Abhandlung des Referenten (Die Erd- 
magnetische Nachstorung, Met. Zeitschr. 1895) wird eine tagliche Schwankung 
des Effectes als wahrscheinlich hervorgehoben, ebenso wie die Schwierigkeit, 
den Effect als Folge einer Storung ansehen zu diirfen. 

In einem Appendix schreibt Herr W. Ellis, wie er die Greenwicher Be- 
obachtungen 1890-94 nach gleichen Principien schon teilweise bearbeitet hat 
und es sich herausgestellt hat, wie der non-cyclic Effect der Hauptsache nach 
sich gleichartig zeigt, jedoch mit zuweilen betrachtlichen Unterschieden der 
individuellen Zahlen. W. van Bemmelen. 

6 77 



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78 REVIEWS [vol. n, no. a.] 

Folgheraiter, G. Ricerche suW inclinazione ntagnetica alV epoca elrusea. 
Rendiconti R. Ace. dei Lincei, Roma, Vol. V, 2° setn. 1896, pag. 293. 

Sotto questo titolo l'Autore pubblica i resultati dei suoi studi sul valore 
dell' inclinazione del campo terrestre nell' Italia media circa 8 e 6 secoli a. C, 
valore ottenuto in base alia distribuzione del magnetismo in vasi etruschi di 
argilla attribuiti a quelle epoche. 

Per potere comprendere bene, come l'A. sia riuscito a stabilire, che oggetti 
di argilla cotta hanno funzionato in certo modo da inclinometri registratori 
della direzione del campo terrestre in un' epoca si lontana da noi, si devono 
prendere in esame varie Note, che dallo stesso Autore furono pubblicate negli 
ultimi mesi : l in queste egli dopo aver dato un rapido sguardo alle nostre cog- 
nizioni sopra le variazioni secolari dell' inclinazione magnetica, svolge il con- 
cetto del suo metodo, che e basato : 

i° Sulla propriety che hanno le argille di magnetizzarsi durante la cottura 
e di conservare perennemente e costantemente nella stessa orientazione il mag- 
netismo acquistato per 1' azione induttrice del campo terrestre ; 

2 Sulla possibility di dedurre dalla distribuzione del magnetismo libero, 
che noi troviamo in oggetti di determinate forme, o qual era la loro orienta- 
zione durante la cottura, se conosciamo la direzione del campo che li ha mag- 
netizzati, o vici versa quale e stata la direzione del campo magnetizzante, se a 
noi e nota la posizione data all' oggetto nella fornace. 

Vogliamo ora esporre brevemente, in che modo dall' A. vengono esaminate 
e discusse queste due questioni fundameutali. 

* 

Sia dato un cilindro d' argil la, e suppomamo che esso sia stato cotto tenuto 
in posizione verticale : rappresenti a 6 c d ]& sezione passante per 1* asse, che 
si trovava durante la cottura nel piano del meridiano magnetico (chiamata 
dall' A. per brevita la sezione normale) % ed indichi la 
freccia la direzione del campo. (L'inclinazione nella 
stanza, ove furono fatte le ricerche, era 57 40'.) 

Se ora col metodo delle deflessioni (est-ovest) si 
determina l'intensita del magnetismo libero iiei vari 
punti della periferia delle due basi, si trova alia base 
inferiore solamente magnetismo di polarita nord, che 
varia regolarmente da un valore massimo in a ad un 
minimo in b, ed analogamente alia base sup -ri ore si 
ha solo magnetismo di polarita sud, che varia da un 
minimo in c ad un massimo in d. 
Se il cilindro durante la cottura £ stato inosce disposto coir asse paral- 
lelo alia direzione del campo, collo stesso procedimento si trova alia periferia 
della base inferiore un valore costante, o quasi, in tutti i punti e di polarity 
nord, ed alia periferia della base superiore pure un valore dell' intensity cos- 
tante in tutti i punti ma di polarita sud. 

1 Variazione secolare deW inclinazione magnetica. Rendiconti R. Ace. Lincei, 
Classe Science fis. ecc. vol. V, 20 sem. 1896, pag. 66. 

Determinazione sperimentale della direzione di un campo magnetico uniforme 
dalV orientazione del magnetismo da esso indotlo, ibidem, pag. 127, 199 e 242. 

Sulla forza coercitiva dei vasi etruschi, ibidem, vol. VI, i*> sem. 1897, pag. 64. 




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REVIEWS 79 

Se si esamina ancora la distribuzione del magnetismo dopo di avere collo- 
cato il cilindro durante la cottura col suo asse nel piano del meridiano magne- 
tico e perpend icolare alia direzione del cauipo, si trova in a un massimo nord ; 
da questo punto percorrendo la periferia rintensit& magnetica va successiva- 
mente diminuendo, diventa nulla a circa 90 da a, poi cresce col segno con- 
trario, finchS in b si ha un massimo sud. Continuando l'esame P intensity va 
successivamente diminuendo, diventa nulla a 90 da b y e poi cresce nuova- 
mente, ma con polarity nord, fino in a. L'identica cosa si riscontra alia peri- 
feria superiore : in c vi 6 il massimo nord in d il massimo sud, sicchS a c 6 una 
linea di massima polarita nord, bdla. linea di massima polaritS. sud. 

Risulta chiaro da ci6, che se in successve cotture si cambia la posizione 
del cilindro partendo dalla posizione parallela alia direzione del campo, fino a 
che Passe diventa a questa perpendicolare, anche la distribuzione del magne- 
tismo cambia gradamente in modo, che ad ogni determinate posizione di cot- 
tura corrisponde sempre una determinata distribuzione del magnetismo alia 
periferia delle due basi. Se consciamo quindi l'inclinazione magnetica in un 
luogo, possiamo in base alia distribuzione del magnetismo in un cilindro sta- 
bilire, in quale posizione questo e stato cotto, e viciversa se noi conosciamo in 
qnale posizione e stato collocato l'oggetto durante la cottura, possiamo in base 
alia distribuzione del magnetismo stabilire la direzione del campo. 

L' A. ha pure constatato, che quanto fu detto per i cilindri si verifica anche 
per oggetti, che piu o meno si awicinano ad alcune forme di vasi etrushi : fa 
notare, che a seconda che variano le dimensioni e la forma di essi, si hanno 
delle distsibuzioni del magnetismo, che corrisponderebbero ad un' inclinazione 
della forza magnetizzante un po'di versa dalla reale; ma le lines generali del 
fenomeno non cambiano inai. 1 

Si pud comprendere ora, come anche gli oggetti d' argilla giunti fino a noi 

dalla piu remota antichita ci possano indicare, quale era air epoca e net luogo 

della loro cottura l'inclinazione magnetica, purchS ben inteso si possa stabilire 

la posizione loro data nella fornace, e si possa essere certi, che il magnetismo 

allora in essi indotto non ha punto cambiato orientazione. 

» 
* « 

Per accertarsi che Torientazione del magnetismo negli oggetti di argilla 
cotta antichi non ha punto variato dall' epoca della loro cotturo fino ad oggi, 
r A. ha cercato di avere a sua disposizione degli oggetti rimasti per secoli e 
secoli nell identica posizione, in cui si trovano al presenie, ed ha determinato 
in essi la direzione dell' asse magnetico. A tale scopo ha staccato da vari mat- 
toni, che formano parte degli avanzi di antichi monumenti, ville, sepolcri ecc 
sparsi per Roma e la sua Campagna, un piccolo pezzo di forma a press' a poco 
di parallelepipedo, ed ha avuto cura di fissare con appositi segni l'orientazione, 
che i singoli pezzetti avevano sul monumento. Egli ha trovato che V orienta- 
zione del magnetismo nei diver si pezzi non corrisponde ad una direzione fissa, 
ma varia invece da pezzo a pezzo, senza che ne predomini alcuna. E naturale, 

1 II riassumere il modo di preparare gli oggetti, le precauzioni usate per la cot- 
tura, la via seguita per esuminare la distribuzione del magnetismo libero nei varii 
punti d' un oggetto e per dedurre dalle misure la direzione del suo asse magnetico, 
la discussion e delle cause d'errore e la grandezza di questo non solo ci porterebbe 
troppo in lungo, ma l'esposizione sommaria probabilmente riescirebbe poco chiara, 
e percio per tutte queste questioni rimandiamo il lettore al lavoro ori gin ale. 



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80 REVIEWS [Vol. II. No. a.] 

che se l'induzione terrestre fosse stata capace di cambiare l'orientazione primi- 
tiva del magnetismo in quegli oggetti, questi si dovrebbero trovare ora tuag- 
netizzati tutti nella stessa orientazione. 

Anche l'esame della suppellettile fittile trovata in alcune tombe vergini, 
mai cioe" fino ad ora toccate dall' uomo, delle antiche necropoli di Narce e di 
Fallerii ha dato lo stesso risultato ; e si noti che quella suppellettile £ rimasta 
nella posizione, in cui fu trovata, e quindi a noi nota, per forse 25 o pifl secolL 
Ma v'S di pitl: perchfc a nissitno possa nascere il dubbio, che, se Pazione conti- 
nua dell' induzione terrestre in tanti secoli non £ stata capace di orientare 
nello stesso senso il magnetismo in tutti quegli oggetti, abbia per6 potuto, 
anche solo in piccola parte, modi fie are la distribuzione del magnetismo, 1' A. 
riporta i risultati delle sue misure fatte in Arezzo (vedi ultima Nota citata) su 
vasi, che ci sono pervenuti interi e su altri che furono ricostruiti pochi anni 
addietro coi f rantumi. nei quali erano stati ridotti or son 20 secoli e che rima- 
stro per tutto questo tempo ammucchiati e confusi tra loro. Se in questi 
pezzi il campo terrestre avesse modificato anche di poco l'orientazione del 
magnetismo aumentando in alcuni e diminuendo in altri TintensitS magnetica 
secondo la loro posizione, si dovrebbe trovare nei vasi ricostruiti ora con 
simili pezzi una distribuzione saltuaria e non regolare attorno alia periferia 
della base e della bocca. All'oposto non uno dei vasi restaurati ha mostrato 
distribuzione saltuaria, ma tutti una distribuzione, che varia regolarmente da 
punto a punto come nei vasi trasmessici interi. 

Sarebbe possibile questo risultato, se una modificazione anche piccola del 
magnetismo avesse avuto luogo ? 

A questa propriety dell' argilla di conservare cos! tenacemente il magne- 
tismo T A. da molto peso : prima di tutto perche di ipotetico nei metodo da 
lui adoperato per trovare l'inclinazione magnetica non c'5 assolutamente altro 
che il giudizio, che ora ci facciamo, sulla posizione nella quale i vasi antichi, 
che esaminiamo, furono cotti. In secondo luogo questa proprietS permitteri 
di risolvere con tutta sicurezza non solo il problema sulla variazione secolare 
dell' inclinazione magnetica, ma anche quello dell' andamento della declina- 
zione nei tempi passati, quando si scoprano degli oggetti d'argilla fissi ancora 
nella posizione, in cui mrono cotti, perche in talcaso il piano del meridiano 
magnetico all'epoca della loro cottura doveva corrispondere all' orientazione 
del piano, nei quale ora noi troviamo la loro sezione normale. 

* * 

Circa la posizione data ai vasi antichi per la cottura non si sa nulla di po- 
sitivo : perS vi sono alcune determinate forme di vasi come gli oivoj&u gli 
b'/fioi, le situle ecc, per le quali concorrono tante condizioni favorevoli, perche* 
siano state collocate entro la fornace col loro asse di simmetria verticale, che 
non S ne" ragionevole, ne" possibile ammettere una posizione diversa. Di fatto 
sia per l'economia dello spazio, sia per la necessity di avere uniforme distri- 
buzione di calore attorno ai vasi per ottenere una regolare cottura, sia per la 
necessity che gli oggetti specialmente se forniti di fregi ed ornamenti siano 
collocati in una posizione di massima stability per impedire attriti e sposta- 
menti dovuti alia diminuzione di volume dell' argilla, la cosa pitl semplice e 
pia naturale £ quella di averli fatti poggiare colla loro base o sul fondo della 
fornace, o sopra altri oggetti simili, come operano anche al presente i nostri 
vasai. E siccome la conoscenza della posizione avuta dai vasi durante la cot- 



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REVIEWS 8 1 

tura e* una condizione sine qua non per potere dedurre dalla distribuzione del 

magnetismo la direzione del campo, col 1' A. ha preso in esame unicamente 

quelli, peri quali non si possa dubitare, che sono stati cotti in piedi. 

* 
* * 

Gli oggetti dall'A. esaminati appartengono ai Musei di Villa Giulia in 
Roma e del Conte Senatore Faina in Orvieto. Alcuni sono attribuiti all* 
3° secolo a. C, e forse sono anteriori, altri sono di epoca meno certa, o meglio 
possono appartenere tan to al 5 secolo a. C. come risalire fino all' 8° secolo 
a. C, el' A. stabihto per questi come epoca media 6 secoli a. C. 

Dal complesso delle ricerche risulterebbe che 8 secoli a. C. V inclinazione 
magnetica nell* Italia media era assai piccola e coi poli rovesciati rispetto all' 
attuale, e che forse un paio di' secoli pifi tardi si aggirava attorno al valore o°« 

A questi risultati V A. non vuole dare peso maggiore di quanto meritino 
per le difficolta nella scelta dei vasi, ma certo il metodo ha dei pregi, e potra 
reudere degli utili servigi per allargare le nostre cognizioni sulli variazioni 
secolari degli elementi magnetotellurici. C. Chistoni. 



Carlheim-Gyllenskold, V. Determination des Elements Magnitiques dans 
la SuZde Meridionale pendant Vannie 1892. Upsala, 1896. 

In this publication which was presented to the Royal Society of Sciences 
of Upsala, on October 20, 1896, the Author gives the details of the observa- 
tions made during his second expedition, undertaken to determine the values 
of the terrestrial magnetic elements in the southern part of Sweden. The 
results obtained in his first expedition, in 1886, may be found in the 23d vol- 
ume of the "Me*moires de l'Acad^mie de Stockholm." The instruments em- 
ployed in making the observations are not described in the present memoir. 
They are the same that were used in the earlier work, and are described in 
the account of it. Time was determined throughout the expedition by a single 
chronometer, which was frequently compared with the time of the observatory 
at Stockholm by means of time-signals sent over the Government telegraph 
and telephone lines. The observation spots occupied at each of the one hun- 
dred and thirty observing stations are described in detail. At all these sta- 
tions, except two, the azimuth was established by astronomical observations, 
generally of the sun. On account of the unfavorable weather that prevailed 
during the periods of magnetic observation at Backviken and Billesholms, 
astronomical observations could not be made, so that at these stations resort 
was had to the charts of the Etat-Major for obtaining the azimuths of the 
marks. 

Full tabular statements of the observations are given, and also of the 
resulting values of the horizontal intensity, declination, and inclination, 
reduced to September 1, 1892, by means of the magnetographs of the observa- 
tory at Copenhagen. The Author has evidently written throughout with a 
view of disclosing to others all the details that will contribute to an under- 
standing of the reliability of his results, which are entitled to full faith and 
credit. 

One feature of the work calls for special notice. The observations for in- 
clination were made with a Dover Dip circle without reversing the poles of 
the needle. The observations made by this method had inherent in them the 



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82 REVIEWS [vol. II, no. 2.) 

errors due to defective mechanical suspension of the needle; but observations 
were made to determine the amount of this error at five stations, and, by in- 
terpolation, the error at each of the intermediate stations was found with a 
degree of closeness sufficient to bring the resulting inclinations within the 
usual errors of observation. G. W. Littlehales. 



McAdie, A. Equipment and Work of an Aero-Physical Observatory. Smith- 
sonian Miscellaneous Collections, 1077; Washington, 1897. 

In dieser, zur Bewerbung um den Hodgkins-Yreis der Smithsonian Insti- 
tution 1894 vorgelegten und mit ehrenvoller Erwahnung und der Bronze- 
Medaille ausgezeichneten Denkschrift macht der Verfasser Vorschlage iiber 
die Ausriistung und den Arbeitsplan eines aero-physikalischen Observato- 
riums, d. h. eines Instituts, das sowohl der allseitigen wissenschaftlichen Er- 
forschung der Atmosphare nach ihrem physikalischen und chemischen Verbal- 
ten, nach ihrer Bedeutung fur die Physiologie und Biologie, wie auch der 
praktischen Verwertung der erworbenen Kenntnisse fur die Wetterprognose 
und die Hygiene gewidmet sein soil. 

Dem herkommlichen Inventare der meteorologischen Observatorien wer- 
den u. a. Chwolson's Aktinometer, Langley's Spektro -Bolometer, eine Vorrich- 
tung znr fortlaufenden photograph ischen Aufnahme des Absorptionspektrums 
der Atmosphare, Aitken's Staubzahler und Apparate zur Beobachtung der 
atmospharischen Electrizitat hinzugefiigt Hiermit ist zugleich die umfas- 
sende Anlage des Arbeitsplanes gekennzeichnet 

Besondern Nachdruck legt der Verfasser auf die Notwendigkeit elektri- 
scher Messungen, indem ermit Rechtdie Liickenhaftigkeit der bis jetzt darin. 
erzielten Resultate hervorhebt Es ist dringend zu wiinschen, dass seine Vor- 
schlage, betreffend die Messung der elektrischen Zerstreuung in der Atmo- 
sphare, die Bestimmung des Potentialgefalles in grossern Hohen und die 
Beobachtung der elektrischen Vorgange bei Gewitteru, die verdiente Beach- 
tung finden. 

Die kleine Schrift beriihrt den Leser angenehm durch die Warme, mit der 
der Verfasser fur seinen Plan eintritt. Wenn er an einigen Stellen in den 
Hoffnungen, die an dessen Verwirklichung gekniipft werden, etwas weit geht, 
so ist das durch den Wunsch erklarlich, dem Unternehmen recht viel Freunde 
zu gewinnen. 

Zu dem Teile der Arbeit, der von der atmospharischen Elektrizitat han- 
delt, mogen einige Bemerkungen Platz finden. Die auf Seite 15 erwahnte 
starke Zerstreuung der negativen Elektrizitat auf dem Sonnblick ist, wie in 
der citierten Abhaudlung naher begriindet wird, nicht mit Sicherheit auf die 
Wirkung des Sonnenlichts zuriickzufiihren. In der ersten Tabelle, Seite 16, 
fehlt die zum Verstandniss notwendige Bemeikung, dass v die Anzahl der 
Einzelbeobachtungen bedeutet Der pag. 26 angegebene Betrag des Poten- 
tialgefalles von 4 Volt pro Meter ist irrefiihrend und ohne Zweifel dadurch 
zu Stande gekommen, dass die zu Gruude liegenden Messungen nicht fur das 
homogene elektrische Feld in der Atmosphare gelten. (Referent vermutet, 
dass Beobachtungen an der Spitze und am Fusse des Washington Denkmals 
verwertet worden sind.) Auch der Verfasser bemerkt, dass der auffallend 
kleine Wert wohl durch Storungen der Aquipotentialflachen durch Gebaude 
erklarbar sei. H. Geitbi*. 



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REVIEWS 83 

Henry Gelxibrand. A Discourse Mathematical on the Variation of the 
At agnetical Needle. London, 1635; Berlin, 1897. 

This interesting and elegant reprint, in facsimile, forms Number 9 of the 
valuable series 1 of reprints of books and charts that have been epoch-making 
in the domains of meteorology and terrestrial magnetism, published under 
the editorship of Professor Hellmann, and with the co-operation of the Ger- 
man Meteorological Society. 

This work, the original of which is very scarce, contains, as well known, 
the first indisputable proof of the secular variation of the magnetic declina- 
tion. The reprint has been prepared from the copy in possession of Mr. 
Latimer Clark, F. R. S. Magneticians owe a debt of gratitude to Professor 
Hellmann, and the German Meteorological Society for bringing this work 
within the reach of every one, the price being but three marks. 

L. A. Bauer. 

1 Neudrucke von Sehriflen und Karten uber Meteorologie und Erdmagnetismus. 
Herausgegeben von Professor Dr. G. Hellmann. Berlin, A. Ascher & Co. 



RECENT PUBLIC A TIONS ' 



Arendt, T. Beziehungen der elektrischen Erscheinungen unserer Atmo- 
sphare zum Erdmagnetismus. Reprinted from " Das Wetter," 1896, Nov. 
and Dec. Pp 28. 

Batavia. Observations made at the Magnetical and Meteorological Observa- 
tory during the year 1895. Vol. XVIII; Batavia, 1896; 26x36 cm. [Con- 
tains the customary observations and results for 1895.] 

Bigelow, F. H. Storms, Storm Tracks, and Weather Forecasting. U. S. 
Weather Bureau, No. 114. Washington, 1897. 87 pp. and 20 illustrations. 

Boixer, W. Das Sudlicht. Erste Abhandlung. Beitriige zur Geophysik. 
Bd. Ill, Heft 1. 

Car^heim-Gyllenskold, V. Sur la forme analytique de l'attraction magn£- 
tique de la terre exprimee en fonction du temps. Stockholm, 1896. Pp. 36. 
Inserts, 3. 

Elster, J., und Geitel, H. Zusammenstellung der Ergebnisse neurer Ar- 
beiten uber atinospharische Elektricitat. Wissenschaftliche Beilage zum 
Jahresbericht des Herzoglichen Gymnasiums zu Wolfenbuttel. 1897. 
Progr. No. 726. Wolfenbuttel, 1897. Pp. 24. 

Folgheraiter, G. I punti distinti delle roccie magnetiche e le fulminazioni. 
Nota: Frammenti concernenti la Geofisica dei pressi di Roma. N. 5. 
Roma, 1896. 19x27 cm. Pp. 14. 

Fortschritte der Physik im Jahre 1895. Dargestellt von der Physik. 
Ges. zu Berlin. 51. Jahrg. III. Kosmische Physik. Red. von R. Assmann, 
Braunschweig, 1896. 8»> LHI. Pp. 686. 

1 Not as yet otherwise noticed in the Journal. As the conventional sizes of 
publications vary so considerably, it has been decided to give the actual outside di- 
mensions ; viz., the breath and length, the former being given first. 



i 



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NOTE 

THE ELEMENTARY PULSATIONS OF THE EARTH'S MAGNETISM. 

In a paper, 1 presented to the Berlin Academy on July 30, 1896, Professor 
Eschenhagen gave a preliminary account of his researches regarding the very 
small variations of the earth's magnetism, which he has detected for the first 
time. He has obtained a very sensitive intensity variometer for the registra- 
tion of minute perturbations. It consists of a unifilar magnetometer, in which 
the magnet is a small* magnetized steel mirror, suspended by fine quartz, 
fibres in a copper damper, and made to lie perpendicularly to the magnetic 
meridian by giving a slight twist to the fibres. The fibres should not be too 
thin, for otherwise too many revolutions of the torsion head would be re- 
quired to place the magnetized mirror in the desired position. Prof. E. 
deems it advantageous, however, that several revolutions should have to be 
applied, as thereby the desired degree of sensitiveness is best secured. A 
magnet thus suspended will give, like the bifilar magnetometer, the variations 
of the horizontal component of the earth's magnetism. Although the distance 
of the recording cvlinder was the same as the customary one with the bifilar 
suspension, 1.72 meters, nevertheless the sensitiveness was increased tenfold. 
In the usual method the value of 1 mm. of the ordinate is equal to 3.2 >, it ; 
denote 0.00001 C. G. S., while for the specially constructed instrument the 
value of 1 mm. of ordinate was equivalent to 0.3 >. Moreover, for the ordinary 
recorder a length of abscissa of 20.5 mm. represents one hour, while for the 
special recorder, making nearly one complete revolution in one hour, 20 mm. 
represented five minutes. 

With this very sensitive intensity variometer, and with the rapidly-revolv- 
ing recording cylinder, Prof. E. succeeded in revealing the smallest magnetic 
perturbations — ihe elementary waves, so to speak, of the pulsations of the earth's 
magnetism. By the ordinary methods these minute waves are either entirely 
obliterated by the coarseness of the curves or crowded together. The tiny 
waves, although they were of varying amplitude, nevertheless were all of them 
nearly of the same length. Expressed in time, the distance from comb to 
comb was almost regularly 30 seconds. 

Prof. E. was not able to explain these vibrations on the assumption that 
the needle, by a magnetic impulse, was set in vibration, which continued long 
after the impulse had died out ; for in the first place the vibration period of 
the magnet was only 8.5 seconds, and, secondly, the effect of the copper 
damper was such that, even with large amplitudes, the magnet was brought 
to rest a»ter the lapse of 20 seconds. The favorable location of the Potsdam 
Observatory also excludes completely the influence of electric street-railways, 
etc. He was forced to conclude that a real physical fact had been revealed by 
these researches. 

Observations made since the presentation of the paper have confirmed 
the main conclusion. Whether the wave length of the elementary waves is a 
constant or a variable quantity, is, as yet, somewhat doubtful. In two cases 
waves of 12 to 15 seconds were registered. They occur frequently from 10 a. m. 
to 2 p. m., even on magnetically calm days. On certain days, when the waves 
are especially regular and well-defined, there seem to occur, at certain inter- 
vals, periods of less energetic pulsations. 

The further investigation of this phenomenon in as many places as pos- 
sible, with apparatus of identical construction, is of the utmost importance. 
A plan to this effect was proposed by Messrs. von Bezold and Eschenhagen to 
the International Meteorological Congress, held in Paris last September, and, 
we believe, favorably acted upon. Professor Eschenhagen will be pleased to 
impart any further information to such as will be interested to join with him 
in these most interesting and valuable investigations. The cost of the mag- 
netometer and recording apparatus will be about 400 marks. 

1 Eschenhagen, M. Vber die Aufzeichnung sehr kleiner Variationen des 
Erdmagnetismus. Sitz. ber. d. k. preuss. Akad. d. Wiss. zu Berlin, XXXIX, 1896, 
pp. 965-66 ; 1 plate. 
84 



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Volume II r *' , plumber 3 

Terrestrial Magnetism, September, 1897 



UEBER DIE FEHLER BEI ERDMAGNETISCHEN 
MESSUNGEN. 

Von H. Wild in Zurich. 

Jede Bestimmung der Elemente des Erdmagnetismus stellt eine 
physicalische, bei der Declination auch theilweise eine astronomische 
Afessung dar, und man darf daher erwarten, dass, wie es bei diesen 
tiblich ist, so auch dort nicht einfach bloss das Resultat der Messung, 
sondern auch die Sicker heit desselben — mittlerer oder wahrschein- 
licher Fehler einer einzelnen Messung oder auch des Re suit at s aus 
mehreren gleichartigen Messungen — mitgetheilt werde. Es gilt 
dies sowohl von den absoluten magnetischen Messungen, als auch 
von den blossen Variationsbeobachtungen der erdmagnetischen Ele- 
mente. Diese Sicherheit wird je nach den Umstanden, iiber die 
man nicht immer unbedingt verfugen kann, wie z. B. die Grosse 
der aufzuwendenden Mittel fur Personal und Instrumente, die Art 
der zur Disposition stehenden Localitaten, u. s. w. eine sehr verschie- 
dene sein ; aber ob sie nun grosser oder kleiner sei, in alien Fallen 
wird es fur die Benutzung der betreffenden Daten und insbesondere 
fur ihre Vergleichbarkeit mit andern nothwendig sein, dass man 
iiber den Grad der Genauigkeit oder Zuverlassigkeit derselben vom 
Beobachter unterrichtet werde. 

AngesichU nun der Thatsache, dass nicht bloss bezuglich vieler 
vereinzelter magnetischer Messungen, sondern sogar von den Beob- 
achtungen der Mehrzahl der magnetischen Observatorien keine oder 
nur ungeniigende Angaben iiber die Sicherheit der Resultate vor- 
liegen, diirfte es wohl zeitgemass sein, einmal des Nahern auf alle 
die nahern Aufschliisse hinzuweisen, welche der Beobachter von 
seinen Messungen zu geben hat, damit die Genauigkeit des Resul- 
tats befriedigend festgestellt werden kann. Eine solche Erorterung 
wird vielleicht geeignet sein, die Differenzen etwas aufzuklaren, 
welche man z. B. bei der Vergleichung der Intensitatsmessungen 
mit verschiedenen Instrumenten gefunden hat. 

2 85 



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86 H. WILD [vol n, No. 30 

I. Allgemkine Bemerkungen. 

Wir fassen hier zunachst alle die Umstande zusammen, welche 
auf die Richtigkeit resp. Sicherheit der magnetischen Messungen 
iiberhaupt influiren konnen. 

I. eisenfreiheit der zu dbn instrumenten verwende- 
tbn materialien. Seit man in neuerer Zeit erkannt hat, dass 
das selbst von renommirten Werkstatten fur magnetische Instru- 
mente verwendete Messing oft sehr eisenhaltig war, erscheint es 
durchaus geboten, dass sich der Beobachter selbst jeweilen durch 
sorgfaltige Untersuchung aller Theile seiner Instrumente von der 
geniigenden Eisenfreiheit derselben iiberzeuge und dies ausdriicklich 
angebe. Es geniigt dabei durchaus nicht, dass man, wie es noch 
hie und da geschieht, das ganze Instrument einem Unifilar- oder 
Bifilar- Magnetometer annahere und zusehe, ob es dabei nicht eine 
merkliche Ablenkung hervorbringe; vielmehr ist es, wie eine nahere 
Ueberlegung sofort erkennen lasst, durchaus nothwendig, dass je- 
der Theil des Instrumentes mindestens auf eine solche Entfernung 
dem abzulenkenden Magnet in giinstiger Stellung angenahert werde, 
in welcher derselbe bei den Messungen mit dem Instrument an die 
darin verwendeten Magnete herantritt. Zum Beleg hiefiir will ich 
nur zwei Beispiele aus meiner Erfahrung anfuhren. Der mag- 
netische Theodolith Nr. 38 von Brauer, der 1869 bis 1877 zu den 
absoluten Bestimmungen der Declination in St. Petersburg ver- 
wendet worden war und bei der Priifung durch Annahern als Gan- 
zes an ein Bifilarmagnetometer scheinbar keinen Eisengehalt hatte 
erkennen lassen, ergab wegen zwei schwach eisenhaltigen Schrau- 
ben, mit denen das Magnetgehause auf dem Theodolithen befestigt 
war und welche sehr nahe an den Magnet darin herantraten, um 
4/6 unrichtige Declinationswerthe und um 0.0038 (mm. mg. s.) 
unrichtige Werthe fur die Horizontal-Intensitat. * *Bei der Ver- 
gleichung des von Edelmann nach meinen Angaben construir- 
ten Inductions-Inclinatoriums mit dem grossen ganz eisenfreien 
Inductions-Inclinatorium des Observatoriums in Pawlowsk im 
Jahr 1892 hatte ich zwischen beiden eine mir unerklarliche Differenz 
von 0/6 fur die Inclination gefunden. Als indessen im Winter 
1892 auf 1893 das erste Instrument behufs Verbesserung der micro- 

1 Sieh H. Wild : Erdmagnetische Differenz zwischen St. Petersburg und Paw- 
lowsk. Bulletin de V Acad. Imp. des sciences, T. XXVII, p. 299. Mars 1881. Af Manges 
physiques, tirH du Bulletin, p. 448-451. 



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FEHLER BEI ERDMAGNETISCHEN MESSUNGEN 87 

scopischen Ablesung am Verticalkreis zerlegt wurde, ergab sich bei 
Untersuchung der einzelnen Theile ein.schwacher Eisengehalt des 
Microscophalters, der friiher nicht entdeckt worden war, weil die 
Microscope eine gemigende Annaherung dieses Theils an das Uni- 
filar-Magnetometer beim unzerlegten Instrument verhindert hatten. 
Nach Ersetzung dieses Stiickes durch ein eisenfreies fand Herr 
Dubinskij im Sommer 1893 bei neuer Vergleichung mit dem grossen 
Inductions-Inclinatorium nur eine, innerhalb der Beobachtungs- 
fehler bei ersterem liegende Difierenz von 0/1 zwischen beiden. 1 

Es ist selbstverstandlich, dass bei dieser Untersuchung die Ein- 
pfindlichkeit des zur Priifung verwendeten Unifilar- oder Bifilar- 
Magnetometers der Genauigkeit der mit dem fraglichen Instrument 
auszufiihrenden Messungen anzupassen ist. Soil z. B. bei der Decli- 
nations-Bestimmung eine Sicherheit von ± 2" erzielt werden, so 
muss das Unifilar-Magnetometer noch eine solche Ablenkung sicher 
erkennen lassen, wenn die Arretirungstheile des Declinatoriums 
seitlich dem Magneten des Unifilars bis auf dieselbe Distanz wie 
seinem eigenen Magnet bei der Beobachtung angenahert werden. 

Ein Unifilar-Magnetometer mit 15 cm. langem rohrenformigen 
Magnet, der in eine starkwandige Kupferrohre eingeschlossen ist 
und dessen Spiegel-Bewegung mit Fernrohr und Scale in 4 cm. Ent- 
fernung beobachtet wird, geniigt fiir solche Untersuchungen, da 
man den zu priifenden Gegenstand dem einen Pol des Magnets von 
der Seite leicht bis auf 2 cm. annahern kann. 

2. EISENFREIHEIT DES BEOBACHTUNGSRAUMES. Fur die abso- 
luten magnetischen Messungen ist eine durchaus eisenfreie Localitat 
selbstverstandlich geboten. Nachdem in neuster Zeit gezeigt wor- 
den ist, dass auch Materialien wie Asbest, Portland-Cement, weisse 
Backsteine, gewisse Granit-Sorten, welche man als eisenfrei betrach- 
tet hatte, erhebliche magnetische Eigenschaften besitzen, geniigt es 
nicht, bloss messingene oder kupferne Nagel, Schrauben, Schlosser 
etc. zu verwenden, sondern muss auch eine sorgfaltige vorgangige 
Priifung aller fiir das betreffende Observatorium zu verwendenden 
Baumaterialien empfohlen werden. Ganz besonders ist auch das 
Material fiir die Steinpfeiler, auf welche die Instrumente postirt 
werden, genau zu untersuchen, da diese Theile naher an die Magnete 
herantreten. Dass der Beobachter selbst ebenfalls nur gut verifi- 
cirte unmagnetisehe Kleidung trage, auch zu benutzende Brillen, 

1 Sieh H. Wild : Inductions-Inclinatorium. Meteor ologische Zeitschrift fur 1895. 
S. 42. 



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$& H. WILD (vol. H, no. 3 3 

Bleistifthalter und dergl. auf Eisenfreiheit untersucht habe und end- 
lich Uhren resp. Chronometer, wenn sie nicht ganz eisenfrei sind, 
beim Gebrauch dem/Instrument nur soweit annahere, dass sie nach 
der vorangehenden Priifung keine merkliche Storung bewirken 
konnen, darf wohl als selbstverstandlich betrachtet werden. 

Dagegen habe ich nachgewiesen, dass die Anwendung von 
nicht ganz eisenfreiem Baumaterial bei Gebauden fur tnagnctische 
Variations- Beobachtung en ohne merklichen Schaden zulassig ist. 1 Es 
geniigt, bei alien beweglichen Theilen, wie Thiirschlossern, Ofen- 
thiiren u. s. w. Eisen zu vermeiden, und ebenso keine fixen eisernen 
Gegenstande von solcher Masse anzubringen, dass der in ihnen indu- 
cirte Magnetismus aus der betreffenden Entfernung einen variabeln 
und damit storenden Einfluss auf die Variations-Apparate ausiiben 
konnte. 

Benutzt man in diesen Localitaten zur Beleuchtung den electri- 
schen Strom, so hat es keine Schwierigkeit, sich durch abwechseln- 
des Unterbrechen und Schliessen davon zu uberzeugen, dass die 
Anlage richtig sei d. h. keinerlei storende Einwirkung auf die mag- 
netischen Instrumente stattfinde. 

II. Specieu,B Bemerkungen. 

I. FBHI.BR DER ABSOLUTEN DBCLINATIONSMESSUNG. Gewohn- 

lich bestimmt man bei der eigentlich magnetischen Messung bloss 
den Winkel zwischen dem, durch den suspendirten Magnet gegebe- 
nen magnetischen Meridian und einer Mire, deren Azimut fur sich 
ein fur alle M&le oder von Zeit zu Zeit durch eine besondere astro- 
nomische Beobachtung ermittelt worden ist. 

Man pflegt nun meistens den Fehler der absoluten Declinations- 
messung in der Art zu bestimmen, dass man in kiirzeren Intervallen 
eine Reihe von Messungen des erwahnten Winkels ausfuhrt, als- 
dann unter Voraussetzung unveranderten Zustandes des Unifilar- 
Magnetometers resp. Declinations- Variometers wahrend der ganzen 
Zeit nach gleichzeitigen Beobachtungen oder Registrirungen des 
letzteren die Declinationsvariationen aus den einzelnen absoluten 
Messungen eliminirt und schliesslich aus den Abweichungen der- 
selben vom Mittel in iiblicher Weise den mittleren oder wahrschein- 

1 H. Wild : Beitrage zur Bntwicklung der erdmagnetischen Beobachtungsinstru- 
mente. § 2. Konnen magnetische Variationsapparate in Gebauden aus nicht eisen- 
freiem Material aufgestellt werden ? Repertorium fiir Meteorologie^ Bd. XVII, No. 6, 
Dec. 1893. 



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FEHLER BEI ERDMAGNE1ISCHEN MESSUNGEN 89 

lichen Fehler einer einzelnen Messung ableitet. In diesem Fehler 
sind dann enthalten die Fehler der Einstellung der optischen Axe 
des Fernrohrs auf die Mire einerseits und auf die optische Axe des 
Magnet-Collimators oder auf die Normale des Magnet-Spiegels 
anderseits, ferner eventuelle kleine zeitliche Veranderungen der 
Collimation der magnetischen Axe, wenn nicht bei jeder Messung 
diese Grosse durch Umdrehung des Magnets mit seinem Collimator 
oder Spiegel um 180 eliminirt wird, in welchem Fall dann die 
neuen Einstellungsfehler an Stelle jener Veranderungen treten; 
weiterhin die Fehler bei Aufhebung der Torsion des Suspensions- 
fadens vor jeder Messung resp. Veranderungen in dieser Torsion, 
wenn jene Aufhebung nur von Zeit zu Zeit erfolgt ; sodann Feh- 
ler, welche von einem storenden Einfluss von Luftstromungen itn 
Magnetgehause entstehen konnen und endlich auch der den An- 
gaben des Variationsinstruments anhaftende Fehler, der fur sich zu 
ermitteln ist. 1 

Dagegen ist in dem so ermittelten Fehler nicht inbegriffen der- 
jenige, welchen man bei Bestimmung des Azimuts der Mire be- 
gangen hat und der eventuell durch zeitliche Veranderungen in 
diesem Azimut noch vergrossert werden kann. Da es sich hier um 
absolute Grossen handelt, so ist es offenbar geboten, auch den Be- 
trag dieser beiden Fehlerquellen zu ermitteln resp. anzugeben, da- 
tnit man eine richtige Vorstellung von der Sicherheit des Endresul- 
tates der absoluten Declinationsmessung gewinnen konne. 

2. FEHLER DER ABSOLUTEN INCLINA1IONSMESSUNG. Um den 

Fehler der absoluten Inclinationsmessung zu erhalten, kann man 
ganz entsprechend wie bei der Declination eine Reihe vollstandiger 
Messungen in kurzerer Zeit ausfuhren und wieder nach Elimination 
der Variationen der Inclination aus den gleichzeitigen Aufzeich- 
nungen oder Beobachtungen der Variometer fur Horizontal- und 
Vertical-Intensitat (Bifilar-Magnetometer und Lloyd'sche Wage) die 
Abweichungen der einzelnen Messungen vom Mittel bilden. 

Der hieraus abzuleitende Fehler ist nach Abzug des Fehlers der 
Variometer 2 der wirkliche absolute Fehler der erhaltenen Inclination, 

1 Wie an der Hand des letzteren der eigentliche Fehler der absoluten Declinations- 
messung zu ermitteln ist, habe ich am Schluss meiner Abhandlung: ,,Ueber die Be- 
stimmung der absol. magnet. Declination im Observatorium zu Pawlowsk" {Mint, de 
VAcad. Imp. des sciences de St. PHersbourg, VII. sene, T. XUI, No. 6, 1894) sowie 
auch in meiner Schrift: ,.Das Konstantinow'sche meteorol. und magnet. Observato- 
rium zu Pawlowsk," S. in erortert. 

* Sieh das zweite Citat oben. 



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9Q 



H. WILD [vol. II, No. 3.] 



wenn dieselbe mit dem Indue tions-Inclinatorium nach einer der Me- 
thoden bestimmt worden ist, welche ich in meinem Artikel : „Les 
m^thodes pour determiner correctement Tinclinaison absolue avec 
Tinclinateur & induction et r exactitude obtenue en dernier lieu avec 
cet instrument k TObservatoire de Pawlowsk" * naher erortert und 
zusammengefasst habe. 

Dagegen tritt zu dem so abgeleiteten Fehler, wenn ein Nadel- 
Inclinatorium benutzt worden ist, noch ein ganz unbekannter, be- 
sonders von der Gestalt und Beschaffenheit der Zapfen der Incli- 
nations-Nadel sowie ihrer Unterlage abhangiger Fehler hinzu, der 
mehrere Minuten betragen und beim Gebrauch der Nadel mit der 
Zeit seine Grosse um gleiche Betrage verandern kann. Gewohnlich 
nimmt man an, dass das Mittel der Resultate, welche mit mehreren 
(4 — 6) Nadeln gewonnen worden sind, richtig sei, d. h. dass jener 
unbekannte Fehler, indem er bei den einen Nadeln positiv, bei den 
andern negativsei, im Mittel aller herausgehe. Leider ist auch dies 
thatsachlich nicht der Fall, indem z. B. zwei vorziigliche Dover* sche 
Inclinatorien im Mittel ihrer je 6 Nadeln uns doch noch Unter- 
schiede von 1/3 zeigten und bei dem einen von ihnen das Mittel 
von 4 Nadeln von einem Jahr zum andern sich um 0/55 veranderte.* 

Da es aber unmoglich ist, fur Inclinationen, die mit einem Nadel- 
Inclinatorium erhalten worden sind, einen bestimmten absoluten 
Fehler — wenigstens innerhalb einer Grenze von ± 1' — anzugeben, 
wahrend Inductions- Inclinatorien leicht bis auf d= 0/1 sichere abso- 
lute Werthe liefern konnen, so kann wohl die vollstandige Aus- 
schliessung von Nadel-Inclinatorien aus den erdmagnetischen Be- 
obachtungen nur noch eine Frage der Zeit sein. 

Fur die beiderlei Inclinatorien sind in den oben erwahnten be- 
rechneten Fehlern der Resultate enthalten die aus fehlerhafter Ab- 
lesung der Theilkreise, ferner aus ungenugender Nivellirung der 
Axen sowie aus unvollkommener Orientirung der Rotationsaxe des 
Inductors oder der Drehungsebene der Nadel parallel zum magne- 
tischen Meridian entspringenden Fehler. Da Fehler in der er- 
wahnten Orientirung von o.°5 fur Inclinationen von 75 bis 45 
bloss Unsicherheiten der Resultate von 2 bis 4" bedingen und die 
Inclinatorien vor jeder Messung neu nivellirt zu werden pflegen, so 

1 Bulletin de VAcad. Imp. des sciences de St. PSiersbourg, 1895, Mars, No. 3, 
p. 205. 

1 Sieh Ann. des phys. Central-Observatoriums zu St. Petersburg, Theil I, Bin- 
leitung zu den Beob. von Pawlowsk, 1885 und 1892. 



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FEHLER BEI ERDMAGNETISCHEN MESSUNGEN 



9i 



sind die ersten Fehler durchweg verschwindend klein. Beim Nadel- 
Inclinatorium involvirt endlich der obige Gesammt-Fehler noch 
den aus der Reibung der Nadel-Zapfen an ihrer Unterlage bedingten 
Fehler, und beim Inductions-Inclinatorium den bei den Ablesungen 
der constanten Elongationen der Magnetnadel im Multiplicator oder 
bei Aufsuchen der Stellung der Rotationsaxe des Inductors, wo der 
Strom verschwindet, begangenen Fehler. 

Dass in jenem Gesammt-Fehler auch noch der steckt, welcher 
aus einer ungeniigenden Reduction der Beobachtungen auf constante 
Inclination nach den gleichzeitigen Angaben der Variometer ent- 
springt, haben wir oben bereits angedeutet. 

3. FEHLER DER ABSOMJTEN MESSUNG DER HORIZONTAI,- 

intensitat. Eine einigermassen genaue absolute Messung der 
Horizontal-Intensitat der erdmagnetischen Kraft erfordert fur die 
einzelnen Operationen, aus denen sie sich zusammensetzt, so viel 
Zeit, dass man der Constanz des Erdmagnetismus wahrend derselben 
nicht sicher sein kann und dass daher im Allgemeinen schon bei 
jeder einzelnen Messung die Variationen der Declination und der 
Horizontal-Intensitat vermittelst der gleichzeitigen Angaben der 
betreffenden Variometer zu eliminiren sind. Angenommen es sei 
dies bei einer Reihe innerhalb kiirzerer Zeit ausgefiihrter vollstan- 
diger Messungen geschehen, so lasst sich wieder aus denselben nach 
Elimination der zeitlichen Veranderungen der Horizontal-Inten- 
sitat gemass den Angaben des betreffenden Variometers vermittelst 
der Abweichungen der einzelnen Resultate vom Mittel aller ein 
mittlerer oder wahrscheinlicher Fehler der einzelnen Messung be- 
rechnen. 

Hatte man bei jeder einzelnen Messung jeweilen alle die Grossen, 
welche in der Formel fur die Berechnung der Horizontal-Intensitat 
aus den Beobachtungen compariren, neu bestimmt, so ware der so 
ermittelte Fehler in der That gleich dem absoluten Fehler unserer 
I ntensitats- Messung combinirt mit dem Fehler, welcher den An- 
gaben des Variometers fur die Horizontal-Intensitat anhaftet. Es 
wird indessen Niemand in dieser Weise bei den Messungen ver- 
fahren ; man pflegt vielmehr aus guten Griinden eine grossere oder 
geringere Anzahl der Bestimmungsgrossen durch besondere Beob- 
achtungen ein fur alle Male oder wenigstens nur nach grosseren 
Zeitintervallen, wahrend welcher man sie als constant betrachten 
kann, zu ermitteln. 



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92 H. WILD [vol. ii, no. 3.] 

Nehmen wir z. B. an, es werde die HorizontaMntensitat H mit 
einem magnetischen Theodolith nach der Gauss-Lamont'schen Me- 
thode bestimmt, so dass man hat : 



JTs = 



TV sin 



— { i + (/i + 2 *) *± k - (* + 3 nt) 

in v I 2 



— v(i + sinzO— +»'—-* 1, 

2 2 J 

wo abkiirzend gesetzt wurde : 
x = 0.00004630 1- 0.00002315 0.00003808 V k — 



2 2 ^2 2 

und bedeuten : 
7* die unmittelbar beobachtete Schwingungsdauer des Hauptmag- 

nets, 
v die mittlere Ablenkung, welche dieser in der Entfernung E am 

Hiilfsmagnet hervorbringt, 
Nt das Tragheitsraoment des Hauptmagnets mit seiner Suspension 

bei der Normaltemperatur / ol 
Et Q die Entfernung der Mittelpunkte beider Magnete bei den Ab- 

lenkungsbeobachtungen fiir dieselbe Normaltemperatur, 
p und q die sogenannten Ablenkungsconstanten, von welchen ge- 

wohnlich q durch passende Wahl der relativen Dimensionen 

beider Magnete mit geniigender Annaherung zum Ver- 

schwinden gebracht wird. 
J die Ablenkung des Hauptmagnets aus seiner Gleichgewichtslage 

im magnetiscken Meridian durch eine Torsion des oberen 

Endes des Suspensionsfadens um 360 , ausgedriickt in Mi- 

nuten, 
s den taglichen Gang des zur Bestimmung der Schwingungsdauer 

benutzten Chronometers in Secunden (bei dadurch beschleu- 

nigtem Zuriickgehen des Chronometers als positiv aufgefasst) > 
a das Mittel der Anfangs- und Endamplitude der Schwingungen in 

Graden ausgedriickt, 
k den Enipfindlichkeits-Coefficienten des Variometers fur Horizontal- 

Intensitat, an dem zur Zeit der Schwingungsbeobachtungen 

die mittlere Scalenablesung n s und zur Zeit der Ablenkungs- 

beobachtungen eine solche gleich n a beobachtet wurde, so 

dass 



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FEHLER BEI ERDMAGNETISCHEN MESSUNGEN 



93 



H s die dem Scalentheile n s des Variometers entsprechende Hori- 
zontal-Intensitat, 

v der Langen-Inductions-Coefficient des Hauptmagnets, 

v' der Quer-Inductions-Coefficient des Hauptmagnets, 

* der mittlere lineare thermische Ausdehnungs-Coefficient des Mag- 
nets und seiner Suspension, 

m der lineare thermische Ausdehnungs-Coefficient der Substanz der 
Ablenkungsschiene, 

M der Temperatur-Coefficient des Hauptmagnets, 

t s die Mitteltemperatur des Hauptmagnets und seiner Suspension 
bei den Schwingungsbeobachtungen, 

t a die Mitteltemperatur des Hauptmagnets und der Schiene, auf der 
er liegt, wahrend der Ablenkungsbeobachtungen. 

Zur Elimination der Abweichung der Einstellungs-Marke am 
Hauptmagnet von seinem magnetischen Mittelpunkt und der Ab- 
weichung dieses Mittelpunktes beim Hiilfsmagnet von der Schienen- 
mitte soil der Hauptmagnet stets in 4 Lagen auf die Schiene auf- 
gelegt werden. Bezeichnet man die hiebei nach Einstellung des 
Collimator-Fernrohrs auf den Magnetspiegel erfolgten Ablesungen 
am Horizontalkreis des Theodoliths : 

1. bei Hauptmagnet Ost Nordpol nach Ost gewendet mit <p x 
*• t* >» >» >» 

3- » » West „ 

4* >> »> a >» 

und die gleichzeitigen Ablesungen an den Variationsinstrumenten 

mit: 

n\ ri 2 ri z ri A beim Unifilar-Magnetometer 
v!\ n" 2 n" 3 ri' A beim Bifilar-Magnetometer, 

so ist, wenn e den Winkelwerth eines Scalentheils beim Unifilar- 
Magnetometer darstellt, der gesuchte Ablenkungswinkel v und der 
oben mit n a bezeichnete Scalentheil gegeben durch : 

v _ <Pi — 92 + <f A — <Pz 1 n\ — »'a + n\ — ri z ^ 
4 4 

n a = . 



West 


»> 


» 92 


Ost 


>> 





Gewohnlich werden bei jeder Messung bloss unmittelbar beob- 
achtet die Grossen T, v t t s , t a , d, s, a, n a und n S) so dass in dem, in 

3 



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94 &• WILD [Vol. II, No. 3.] 

der erwahnten Weise abgeleiteten Fehler bloss die bei der Messung 
dieser Grossen begangenen Fehler und ausserdem noch die Un- 
sicherheit der Einstellung der Marke des Hauptmagnets auf den 
die Entfernung E bezeichnenden Strich der Schiene enthalten 
sind. 

Wir wollen diesen Fehler den relativen oder variabeln Fehler 
der einzelnen absoluten Messungen nennen, da er bald nach der 
einen, bald nach der andern Seite von der Wahrheit abweichen und 
sorait im Resultat vieler solcher Messungen i turner kleiner wird. 
Im Allgemeinen pflegen darin die grossten Unsicherheiten die Ein- 
stellung des Hauptmagnets auf der Schiene sowie die Ermittlung 
seiner Temperaturen t s und t a darzubieten. 

Die Fehler nun, welche wir bei der besondern Bestimtnung der 
Grossen N t E y p y q, /*, a> m t v, / und k begehen, konnen wir als 
constant e bezeichnen und erst wenn wir deren Einfluss auf das 
Messungsresultat mit dem des vorstehenden relativen Fehlers ver- 
binden, erhalten wir dann den eigentlichen absoluten Fehler der In- 
tensitatsmessung. Nun ist aber die Bestimmung gerade dieser Con- 
stanten eine relativ viel schwierigere und deshalb auch unsicherere, 
so dass der bisweilen allein angegebene relative Fehler der Intensi- 
ty tsmessungen durchaus keine Vorstellung von dem eigentlichen 
absoluten Fehler gewahren kann. Dem Umstand nun, dass man 
haufig die bei Ermittlung dieser constanten Grossen begangenen 
Fehler gar nicht beriicksichtigte, ist meines Erachtens jedenfalls ein 
grosser Theil der Differenzen der mit verschiedenen Instrumenten 
erhaltenen Intensitatswerthe beizumessen. Es erscheint mir daher 
nicht uberfliissig, hier diese letzteren Fehler noch etwas naher zu 
erortern. 

Den Temperatur-Coefficienten /1 des Hauptmagnets leitet man 
gewohnlich aus Schwingungsdauer- oder aus Ablenkungs-Beob- 
achtungen desselben bei zwei verschiedenen Temperaturen ab und 
nimmt dann fur die Ausdehnungs-Coefficienten a und tn die in physi- 
calischen Tabellen-Werken fiir die betreffenden Substanzen — Stahl 
und Messing — gegebenen Daten. Stellt man aber vollstandige 
absolute Messungen mit dem Theodolithen bei zwei verschiedenen 
Temperaturen an, so kann man aus den beiderlei Schwingungs- 
beobachtungen fiir den Werth von i*. + 25 und aus den Ablenkungs- 
beobachtungen fur sich den Werth von // + 3 m berechnen d. h. 
gerade die Coefficient-Combinationen finden, wie sie im Ausdruck 
fur /•, vorkommen. Da aber /* selbst wieder eine Function der 
Temperatur ist, so darf man sich im einen und andern Fall von der 



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FEHLER BEI ERDMAGNET1SCHEN MESSUNGEN 



95 



Normaltemperatur t Q nach der einen und andern Seite nur um eine 
Grosse entfernen, welche gegeben ist durch : 



-■=4-< 



2_ i_H 
M H' 



wo ;i den Temperatur-Coefficienten des Magnets bei der Normal- 
temperatur / und c den Factor darstellen, der seine Aenderung fiir 

i ° Erhohung oder Erniedrigung der Temperatur angiebt. —ry aber 

reprasentirt die Genauigkeit im Verhaltniss zur ganzen Horizontal- 
Componente, welche man bei ihrer Messung zu erzielen wiinscht. 
Setzen wir hier c — o.oi, was in Wirklichkeit sehr nahe der Fall ist, 
und fi Q = 0.0004, so kommt fur 

—rj = 0.0002, und —77- = 0.00002, / — t = zb 3. 2. 

Selbstverstandlich muss dann auch bei den Intensitatsbeob- 
achtungen diese Grenze bei den Abweichungen von der Normal- 
temperatur nicht uberschritten werden, wenn man nicht zu quadra- 
tischen Gliedern der Temparatur beim Temperatur-Coefficienten 
iibergehen will. 

Der Langen-Inductions-Coefficient v lasst sich, wenn am Theo- 
dolith die Einrichtung dazu vorhanden ist, mit ganz geniigender 
Genauigkeit nach der Lamont'schen Methode bestimmen, da man 
jetzt bekanntlich nicht mehr zwischen dem Coefficienten fiir Ver- 
starkung und Schwachung zu unterscheiden hat, oder in Ermang- 
lung dessen lasst er sich auch mit dem Bifilar-Magnetometer oder 
einem Bifilar-Theodolith durch Ablenkungen in der ersten Haupt- 
lage zu diesera ermitteln. 1 Den Quer-Inductions-Coefficenten v' aber 
kann man mit geniigender Annaherung stets =0.1 . v setzen. 

Was den Empfindlichkeits-Coefficient k des Bifilar-Magnetometers 
betriffl, so werden wir dariiber bei den Variationsapparaten das 
Nahere beizubringen haben. 

Damit die Constante q % wie wir oben bemerkt haben, gleich Null 
werde, muss bekanntlich die Lange des Hiilfsmagnets 0.467 der 
Lange des Haupmagnets betragen. Eigentlich gilt dies nur fiir das 
Verhaltniss der unbekannten Polabstande bei beiden Magneten und 
damit diese Bedingung mit geniigender Annaherung auch auf die 

1 Die Methode von W. Weber und ebenso die von mir angegebene Methode zur 
Bestimmung dieser Grosse setzen weitere, in magnetischen Observatorien gewohn- 
lich nicht vorhandene Hulfsmittel voraus. 



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96 H. WILD [vol. li, no. 3.] 

ganzen Langen derselben zu iibertragen sei, muss jeden falls die 
Form und Qualitat beider Magnete eine gleichartige sein. Dieser 
Umstand wird haufig ausser Acht gesetzt und als Htilfsmagnet ein 
solcher von ganz abweichender Form und anderm Stahl gewahlt. 

Die Ablenkungsconstante p pflegt man entweder nach Gauss aus 
dem Resultat dadurch zu eliminiren, dass man jeweile Ablenkungs- 
beobachtungen in zwei verschiedenen Entfernungen der beiden 
Magnete ausfiihrt, wo dann in der Formel fur H 5 statt des Gliedes 
mit p je die beiden Ablenkungswinkel v x und v 2 und die entsprechen- 
den Entfernungen E x und E 2 der Magnete auftreten, oder man leitet 
aus besondern Ablenkungsbeobachtungen dieser Art ein fur alle 
Male den Werth vonp ab und setzt ihn jeweilen bei den einzelnen 
Intensitatsmessungen in die Formel fur H s ein. Das letztere Ver- 
fahren diirfte vorzuziehen sein, da die Bestimmung von/ resp. seine 
Elimination wegen der Kleinheit des Ablenkungswinkels in der 
grossern Entfernung der Magnete eine recht unsichere ist und da- 
her erst das mittlere Resultat von p aus vielen Bestimmungen der 
Art (ungefahr 20) eine hinreichende Genauigkeit erhalt. 

Ganz dasselbe gilt auch von der Ermittlung des Tragheits- 
moments N des Hauptmagnets, wenn sie in der ublichen Weise so 
erfolgt, dass man seine Schwingungsdauern mit und ohne Belastung 
durch einen Korper von bekanntetn Tragheitsnioment misst oder 
nach Gauss drei Schwingungsdauern, namlich ohne Belastung des 
Hauptmagnets und unter Belastung mit Gewichten in zwei ver- 
schiedenen Entfernungen von der Drehungsaxe beobachtet. Auch 
da erlangt erst das Mittel einer grossern Zahl von Messungen (un- 
gefahr 20) eine geniigende Genauigkeit. Geben wir indessen dem 
Magnet und seiner Suspensionsvorrichtung, wie dies im ersten Fall 
mit dem Belastungskorper der Fall ist, eine solche Gestalt, dass wir 
auch aus ihrem Gewicht und ihren Dimensionen das Tragheits- 
moment berechnen konnen, so fallt die aus der Bestimmung der 
zweierlei Schwingungsdauern resultirende Unsicherheit fort und es 
bleibt bloss neben den Fehlern der Abmessung und Wagung noch 
der Fehler bestehen, welcher durch eine nicht homogene Massen- 
vertheilung im Korper bedingt wiirde. Dieser Fehler diirfte aber 
bei einem cylindrischen Magnet kaum grosser sein als bei einem 
Messingcylinder oder Messingring. Von dieser Fehlerquelle ist nur 
das Gauss'sche Verfahren frei, dafiir resultiren aber aus der Noth- 
wendigkeit, drei Schwingungsdauern zu bestimmen, aus eventuel- 
len eigenen Schwingungen der aufgehangten Gewichte und aus Ver- 
anderungen des Luftwiderstandes durch die letztern neue Unsicher- 



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FEHLER BEI ERDMAGNETISCHEN MESSUNGEN 



97 



heiten, deren Gesammtbetrag vielleicht jene Fehlerquelle erheblich 
iibersteigt. Setzt man aber statt der angehangten Gewichte nach 
W. Weber durchbohrte Cylinder auf verticale Stifte am Magnet- 
trager, so bringt man offenbar obige Fehlerquelle wieder herein, da 
man nicht sicher weiss, ob der Schwerpunkt der Cylinder wirklich 
in die Axe der Bohrungen fallt. 1 — Welches dieser Verfahren zur 
Bestimmung der Grosse N man also audi einschlagt, so bleibt da 
immer die Moglichkeit eines kleinen constanten absoluten Fehlers 
bestehen, dessen Betrag man zur Zeit noch nicht genau fixiren kann. 

Die Abmessung der Entfernung der Striche auf der Ablenk- 
ungsschiene, welche die Distanz E resp. ZT X und E 2 der beiden 
Magnete definiren, vermittelst eines Langen - Comparators nach 
einem Normalmeter wird sich leicht mit geniigender Genauigkeit 
ausfiihren lassen. Damit aber die so gemessene Grosse auch wirk- 
lich der Entfernung h der Magnetmittelpunkte entspreche, muss 
eben nicht bloss, wie friiher angedeutet wurde, der Hauptmagnet 
beiderseits vom Hiilfs magnet aufgesetzt, also 2 E gemessen wer- 
den, sondern es darf der Hauptmagnet auch nicht erheblich iiber 
der getheilten Schiene aufgelagert werden, weil sonst die unver- 
meidliche Durchbiegung der letztern die wirkliche Entfernung der 
Magnete gegemiber den Strichen auf der Schiene vergrosserten und 
so ein constanter Fehler entstehen wiirde. 1st aber eine Stellung 
der Magnete in grosserer Hohe iiber der Schiene aus Constructions- 
riicksichten geboten, so muss, wie ich es in meiner Abhandlung 
"Verbesserte Constructionen magnetischer Unifilar-Theodolithe n 2 
vorgeschlagen habe, die Entfernung derselben jeweilen direct ge- 
messen werden, um den aus der Durchbiegung entstehenden Fehler 
zu vermeiden. 

Die Anwendbarkeit der Formel fur H s setzt endlich noch einige 
Bedingungen voraus, deren ungeniigende Erfiillung auch zu Feh- 
lern im Resultat Veranlassung geben konnte. Es sollen namlich 
darnach die magnetischen Axen der Magnete nicht bloss jeweilen 
horizontal liegen, sondern auch bei den Ablenkungsbeobachtungen 
in dieselbe Horizoutalebene fallen, und dabei soil die Verlangerung 
der magnetischen Axe des Hauptmagnets den Mittelpunkt des 
Hiilfsmagnets treffen und auf dessen magnetischer Axe senkrecht 

1 Ich verweise hier blo99 auf die Bemiihungen von Dorn {Wiedemann's Ann. 
Bd. 17, S. 788. 1882) und von Kreichgauer {W. A., Bd. 25, S. 273. 1885), die Fehler 
dieser Methode zu verkleinern, da sie den Wunsch nach Verbesserung bestehen lassen. 

1 Memoires de VAcad. Imp. des sciences de St. PHersbourg^ VIII. sene, Vol. Ill* 
No. 7, Fevrier 1896. 



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98 H. WILD ivol. ii, No. 3.3 

stehen. Der Beobachter wird also auch iiber diese Punkte Auf- 
schluss zu geben haben. 

Wie bereits angedeutet konnen wir auch diese sogenannten cou- 
stanten Grossen nicht unbegrenzt als solche betrachten. So scheint 
z. B. die Ablenkungsconstante p t welche von der Vertheilung des 
Magnetistuus in den beiden Magneten abhangt, mit der Zeit Ver- 
anderungen zu erleiden, welche die Fehlergrenze fur genaue Mes- 
sungen von H iiberschreiten. 1 Es ist also geboten, dieselben in 
langern Intervallen wieder neu zu bestimmen. 

Es darf endlich nicht unterlassen werden, sich richtiger absolu- 
ter Einheiten fur die drei wesentlichen Bestimmungsgrossen, der 
Zeitsecunde \ der Masse des Gramms und der Lange des Centimeters 
zu versichern. Die letztern Grossen sind selbstverstandlich mittel- 
bar auf die neuen internationalen Prototypen des Kilogramms und 
des Meters zu beziehen. Da wir, um eine Sicherheit von z. B. 
0.0001 des ganzen Werthes der Horizontal-Intensitat zu erzielen, 
die Langen E und die Dimensionen des Hauptmagbets oder des 
Hiilfskorpers fur die Tragheitsmoment-Bestimmung bis zu dz 0.0 1 
mm. genau zu messen haben, so diirfen auch die Theilungsfehler 
der benutzten Maassstabe nicht ausser Acht gelassen werden. 

Fassen wir Alles zusammen, so hat also der Beobachter, um eine 
Beurtheilung der absoluten Genauigkeit seiner Resultate fur die 
Horizontal-Intensitat zu ermoglichen, nicht bloss den oben definir- 
ten relativen Fehler seiner Messungen, sondern ausserdem auch 
noch diejenigen der erwahnten Constanten sowie die Sicherheit der 
Beziehung auf die absoluten Einheiten der Zeit, der Masse und der 
Lange anzugeben. 

4. FEHLER DES DECLINATIONS-VARIOMETEES. Es ist noch viel- 

fach die Ansicht verbreitet, dass der einzige Fehler des Unifilar- 
Magnetometers oder Declinations- Variometers,nachdem seine Fa- 
den-Torsion aufgehoben und der Winkelwerth eines Theils seiner 
Scale bestimmt ist, bloss im Ablesungsfehler dieser Scale bestehe, 
oder 0.1 Scalentheil nicht iibersteigen konne. Dies ist indessen in 
Wirklichkeit nur dann der Fall, wenn im Gehause des Instruments 
keine erheblichen Luftstromungen stattfinden, wenn die Torsion 
des Authangefadens nicht starkere zeitliche Veranderungen erfah- 
ren hat, oder durch Temperaturvariationen, Bewegung der Pfei- 
ler und dergleichen nicht Versetzungen von Apparat-Theilen erfolgt 
sind. Die gleichzeitige Ablesung der Scale an einem, am Variome- 

1 Sieh H. Wild: Das Konstantinow'sche meteorologische und magnetische* 
Observatorium in Pawlowsk (bei Petersburg). Petersburg 1895, S. 115. 



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FEHLER BEI ERDMAGNETISCHEN MESSUNGEN 



99 



ter befestigten fixen Spiegel kann offenbar nur iiber einen geringen 
Theil dieser Stromungen Aufschluss geben und durch Beziehen der 
Beobachtungen am Magnetspiegel auf diesen Fixpunkt oder den 
sogenannten Normalstand die Elimination derselben gestatten. 
Waren die absoluten Declinationsmessungen vollkommen genau, 
so konnten sie iiber den Betrag jener Stromungen wenigstens jewei- 
len fur den betreffenden Zeitpunkt am besten Aufschluss geben ; da 
dies indessen nicht der Fall ist, sondern wir gerade uragekehrt die 
Fehler der absoluten Messungen durch Vergleich mit dem als con- 
stant vorausgesetzten Variometer abzuleiten pflegen, so bleibt zur 
genauern Fehlerbestimmung der Variometer nur iibrig, die An- 
gaben zweier solcher, wo moglich etwas verschieden construirter, 
vielleicht auch in verschiedenen Raumen aufgestellter Apparate 
zu vergleichen. Derartige Vergleichungen im Observatorium zu 
Pawlowsk haben nun gezeigt, dass sorgfaltig construirte, gut aufge- 
stellte und vor raschen Temperatur-Aenderungen geschiitzte, mit 
starken Kupferdampfern versehene Unifilar-Magnetometer in der 
That nur mittlere Fehler ihrer relativen Angaben besitzen, welche 
o.i Scalentheil entsprechen, wenn sie durch dieselben absoluten 
Declinationsmessungen controlirt werden und die Magnete in ihnen 
entweder an dtinnen Metalldrahten (Neusilber) aufgehangt sind oder 
dann bei Beniitzung von Coconfaden der storende Einfluss variabler 
Feuchtigkeit im Local auf dieselben durch nahezu luftdichten Ab- 
schluss des Gehauses und Austrocknen desselben durch Schwefel- 
saure aufgehoben ist. 1 Werden ferner, wie das im Observatorium 
zu Pawlowsk der Fall war, allwochentlich absolute Declinations- 
messungen zur Controle ausgefiihrt, deren Sicherheit nicht geringer 
ist als der o.i Scalentheil des Variometers entsprechende Winkel- 
werth, so ist auch der Fehler der aus einer einzelnen Bcobachtung am 
Variometer abzuleitenden Declination von der Ordnung des Winkel- 
werthes von o.i Scalentheil, wenn in der Formel fur Berechnuug 
der letzteni aus der Scalenablesung als Normalstand das Mittel aus 
den 4 Normalstanden benutzt wird, welche aus den allwochent- 
lichen Declinationsmessungen im betreffenden Monat sich ergeben 
haben. 2 Da aber hiebei gewohnlich ein constantes Azimut der 
Mire benutzt wird, so ist der Fehler in der Bestimmung des letz- 
tern noch besonders in Rechnung zu bringen. 

Es ist daher zur genugenden Bestimmung der Sicherheit der 
aus den Beobachtungen am Unifilar-Magnetometer abzuleitenden 

1 Sieh die oben citirte Beschreibung des Observatoriums in Pawlowsk, S, ioi u. 102. 
* Ebenda S. in. 



Dii 



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IOO H. WILD (Vol. U, No. 3.) 

Declinationen nicht bloss eine allwochentliche Controle durch abso- 
lute Declinationsraessungen, sondern wo moglich auch die Beobach- 
tung an zwei Unifilar-Magnetometern und ihr Vergleich geboten. 
Wo dies nicht angeht, hat aber der Beobachter mindestens die aus 
den absoluten Declinationsmessungen zu berechnenden Normal- 
stande des Variometers anzugeben, um wenigstens eine angenaherte 
Beurtheilung der Sicherheit der Angaben des letztern zu ermog- 
lichen. Von Zeit zu Zeit sollte auch der Winkelwerth eines Scalen- 
theils mit Angabe seines Fehlers neu bestimmt werden. 

5. FEHLER DES VARIOMETERS FUR HORIZONTAL - INTENSITAT. 

Wegen der grossern Complicirtheit dieser Variometer gilt hier 
noch in hdhertn Maasse als bei denjenigen fiir die Declination, dass 
man nicht ohne Weiteres die den Ablesungsfehler von 0:1 Scalen- 
theil entsprechende Empfindlichkeit des Instruments resp. die die- 
ser Grosse entsprechende Aenderung der Horizontal-Intensitat als 
Fehler der Angaben des Variometers betrachten kann. Ausser den 
schon beim Declinations - Variometer erwahnten Umstanden hat 
namlich hier auch noch die Veranderung des Stabmagnetismus (sei 
es des bifilar aufgehangten Magnets beim Bifilar-Magnetometer, sei 
es der Deflector-Magnete beim Variometer mit Deflectoren) mit der 
Temperatur und im Laufe der Zeit einen storenden Einfluss. 

Die sehr betrachtliche modificirende Einwirkung der Feuchtig- 
keit bei Aufhangung des Magnets an zwei Coconfaden kann durch 
nahe luftdichten Abschluss des mit Schwefelsaure ausgetrockneten 
Gehauses oder besser durch Benutzung von Metalldrahten statt der 
Coconfaden beseitigt werden und der storende Einfluss der Tempe- 
ratur-Aenderungen lasst sich durch mehr oder minder vollstandige 
Compensation auf ein Maass reduciren, welche eine hinreichend 
genaue bezugliche Correction der Beobachtungen gestattet. Die 
zeitlichen Aenderungen aber des Stabmagnetismus und zugleich 
beim Bifilarmagnetometer die Verlangerung der Suspensionsfaden 
mit der Zeit sind, ausser etwa gleich in der ersten Zeit nach Auf- 
stellung der Apparate, wo die starkste Abnahme des magnetischen 
Moments erfolgt, vermittelst der absoluten Intensitatsmessungen 
geniigend sicher aus den Resultaten zu eliminiren. 

Das beste Kriterium fur die Genauigkeit der aus den Ablesun- 
gen am Variometer abzuleitenden relativen Werthe der Horizontal- 
Intensitat bietet wieder die Vergleichung der Angaben von zwei 
verschiedenen Instrumenten der Art dar. Derartige Vergleichun- 
gen von drei sehr guten Bifilarmagnetometern im Obser\ r atorium 



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FEHLER BEI ERDMAGNETISCHEN MESSUNGEN IO i 

zu Pawlowsk haben ergeben, dass der relative Fehler bei ihnen nicht 
o.io sondern 0.13 bis 0.14 Scalentheilen entspreche. Dieser Fehler 
wird durch die zeitlichen Aenderungen der Instrumente etwas ver- 
grossert, wenn wir aus den Ablesungen an den Bifilaren zugleich 
absolute Werthe der Horizontal-Intensitat ableiten wollen. Wenn 
man wie oben beim Declinations -Variometer so auch hier als Nor- 
malstand in die Formel fiir Berechnung der Intensitat aus den Sca- 
len- und Temperatur - Ablesungen das Mittel der 4 im Laufe eines 
Monats aus den absoluten Intensitatsmessungen abgeleiteten Nor- 
malstande des Variometers einfiihrte, so ergab sich bei obigen In- 
strumenten ein 0.15 bis 0.16 Scalentheil entsprechender Fehler der 
aus einzelnen Ablesungen an ihnen abzuleitenden absoluten Werthe 
der Horizontal-Intensitat. Selbstverstandlich sind in diesem Feh- 
ler die bei den absoluten Intensitatsmessungen begangenen constan- 
ten Fehler, von denen wir sub. 3 gesprochen haben, nicht inbegrif- 
fen, sondern jeweilen noch besonders zu beriicksichtigen. 

Hier ist endlich noch viel mehr als beim Declinations- Variome- 
ter geboten, auch iiber den Fehler der Empfindlichkeits-Bestim- 
mung sei es nun, dass dieselbe z. B. beim Bifilar-Magnetometer aus 
dem sogenannten Torsionswinkel und dem Winkelwerth eines Sca- 
lentheils, oder dann aus Ablenkungsbeobachtungen am Bifilar- und 
Unifilar-Magnetometer abgeleitet werde, Naheres beizubringen. Die 
zweite Methode erheischt theoretisch, 1 wenn sie richtige Resultate 
liefern soil, bei den beiden letzten Instrumenten durchaus gleiche 
Magnete, was haufig ganz ausser Acht gelassen wird. 

In gesteigertem Maasse sind also in Betreff des Variometers fur 
die Horizontal-Intensitat an den Beobachter die beim Declinations- 
Variometer erwahnten Anforderungen zu stellen, um eine Beurthei- 
lung der Zuverlassigkeit seiner Angaben zu ermoglichen : Allwo- 
chentliche absolute Messungen der Horizontal-Intensitat und Mit- 
theilung der daraus abgeleiteten Normalstande des Variometers; 
wo moglich, wenigstens zeitweise, gleichzeitige Beobachtungen an 
zwei Variometern dieser Art ; nahere Angaben iiber die Empfind- 
lichkeitsbestimmung, iiber Einrichtung und Aufstellung der Vario- 
meter, iiber deren Temperaturcoefficienten u. s. w. 

6. FEHLER DES VARIOMETERS FUR VERTICAL-INTENSITAT. Fiir 

die Inclination hat Kupffer ein fiir die damalige Zeit vorziigliches 
Variations-Instrument durch Gambey construiren lassen, welches 
gemass seiner vollkommen guten Erhaltung im Jahr 1878 im Ob- 

1 Sieh H. Wild: Neue Form magnet. Variationsin9tramente etc., S. 30. M£m. 
de VAcad. Imp. des sc. Vile sene, T. XXXVII, No. 4. Mai 1889. 

4 



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102 **• WILD [VOL. II, NO. 3 ) 

servatorium zu Pawlowsk zur erneuten Priifung aufgestellt und ein 
Jahr lang regelmassig beobachtet wurde. Aus der Vergleichung 
mit andern Variometern und den absoluten Inclinations-Messungen 
ergab sich fiir dasselbe als mittlerer Fehler einer Beobachtung 
±: 0/30. 1 Seither hat man die directen Variometer fiir Inclination 
verlassen und sie durch solche fur die verticale Componente der 
erdmagnetischen Kraft ersetzt, da sie einen hoheren Grad von 
Sicherheit darbieten. Unter diesen kann zur Zeit nur die nach 
ihrem Erfinder sogenannte Lloyd sche Wage als hinlanglich be. 
wahrt in Betracbt kommen ; auf sie werden sich also auch allein 
unsere nachstehenden Erorterungen beziehen. 

Das Variometer fiir Vertical-Intensitat resp. die Lloyd'sche 
Wage ist einer Reihe von storenden Einfliissen ausgesetzt, welche 
neben der Schwere einerseits und der Grosse der Vertical-Inten- 
sitat anderseits seine zu beobachtende Gleichgewichtslage bedingen 
resp. modificiren. Vor Allem ist es wieder der mit der Temperatur 
und mit der Zeit variirende Stabmagnetismus, der eine bedeutende 
storende Einwirkung ausiibt ; sodann entstehen Fehler in den An- 
gaben durch eventuelle Verriickung der Schneide des Magnetwage- 
balkens auf ihrer ebenen Unterlage — wenn der Magnet wie iiblich 
senkrecht zum magnetischen Meridian orientirt ist, so strebt er bei 
jeder Erschiitterung sich in denselben hereinzudrehen ; es ist aber 
durchaus die Orientirung seiner magnetischen Axe parallel dem 
Meridian vorzuziehen — , ferner durch die Reibung der Schneiden- 
Axe an ihrer Unterlage, durch Luftstromungen im Gehause und 
endlich auch durch Lageanderungen in einzelnen Theilen des Appa- 
rats, Scale und Fernrohr inbegriffen. 

Da gerade die Lloyd'sche Wage in viel hoherem Maasse ein Va- 
riations-Thermometer als ein Variometer fiir die Vertical-Intensitat 
darstellen wurde, so ist bei ihr eine annahernde Temperatur-Com- 
pensation durchaus geboten, so dass der iibrig bleibende Tempera- 
tur-Coefficient gering wird und so die darnach anzubringende Cor- 
rection klein ausfallt. Die absoluten Messungen der Inclination 
aber in Verbindung mit den gleichzeitigen, dem Bifilar-Magneto- 
meter zu entnehmenden Horizontal-Intensitaten liefern hinlanglich 
genaue absolute Werthe der Vertical-Intensitat, um daraus jeweilen 
die Normalstande der Lloyd'schen Wage zu bestimmen und so die 
zeitlichen Veranderungen des Stabmagnetismus, Verstellungen von 
Apparat-Theilen zu erkennen und zu eliminiren. 

Auch hier ist wieder die Vergleichung der gleichzeitigen Anga- 
ben zweier oder mehrerer Instrumente dieser Art das beste Mittel, 

1 Sieh die obcn citirte Besch reibung des Observatoriums zu Pawlowsk, S. 105. 



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FEHLER BEI ERDMAGNETISCHEN MESSUNGEN 



103 



ihre Leistungsfahigkeit genauer kennen zu lernen. Die Controle 
ihrer Normalstande durch dieselben absoluten Messungen schliesst 
auch hier wieder beim Vergleich die absoluten Fehler der letztern 
aus, so dass wir nur die relativen Fehler der zu vergleichenden Va- 
riometer erfahren. Derartige Vergleichungen im Observatorium zu 
Pawlowsk haben ergeben, dass bei guten Lloyd'schen Wagen der 
mittlere Fehler einer Beobachtung dem Intfcnsitatswerth von 0.28 
Scalentheilen entspreche, der bei weniger vollkommenen Instru- 
menten aber bis 0.6 Scalentheile anwachsen konne. 1 Dieser relative 
Fehler wird wieder in Folge der zeitlichen Veranderungen des Va- 
riometers vergrossert, wenn wir absolute Werthe der Vertical-Inten- 
sitat aus einzelnen Ablesungen an ihnen ableiten wollen. Unter der 
Voraussetzung von allwochentlichen absoluten Inclinationsbestim- 
mungen und entsprechender Controle des Bifilar-Magnetometers 
stieg dann bei den erstern guten Instrumenten der absolute Fehler 
bis zu dem 0.32 Scalentheil entsprechenden Werth an. 8 

Da man dem Magnet- Wagebalken der Lloyd'schen Wage haufig 
eine ganz andere Gestalt und Grosse zu geben pflegt als demjenigen 
des Bifilar- und Unifilar-Magnetomers, die Empfindlichkeit aber der 
Lloyd'schen Wage befriedigend nur durch Ablenkungsbeobachtun- 
gen an ihr und am Unifilar-Magnetometer vermittelst eines Magnets 
in der zweiten Hauptlage zu bestimmen ist, so ist hier noch mehr 
als beim Bifilar-Magnetometer auf die Fehlerquelle hinzuweisen, 
welche aus der Ungleichheit jener Magnete entspringen kann. Wie 
sehr die friiher erwahnte theoretische Anforderung zu beachten ist, 
erhellt wohl am besten aus folgendem Beispiel. Bei alteren Edel- 
mann'schen Variations-Apparaten im Observatorium zu Pawlowsk 
hatten die Magnete des Unifilar- und Bifilar-Magnetometers zwar 
eine nahe gleiche Form und Grosse, indem sie Parallelopipede von 
100 mm. Lange, 20 mm. Breite und 2.2 mm.Dicke darstellten, da- 
gegen der Magnet der Lloyd'schen Wage hatte eine Lange von 200 
mm., nahe 4 mm. Dicke, war in der Mitte breiter und gegen die 
Enden zu schmaler. Empfindlichkeitsbestimmungen durch Ablen- 
kungen an dieser Lloyd'schen Wage und obigem Unifilar-Magneto 
meter im Marz 1893 8 ergaben fur erstere als Aenderung der Vertical 
Intensitdt pro Scalentheil (mm. mg. s.) : 

0.000574 fur eine Entfernung der Magnetcentren : 380 mm. 
und 0.000637 „ „ „ „ „ 580 „ 

1 1. c. S. 104. * ebenda S. in. 

8 Sich Annalen des phys. Central- Observatoriums pro 1892, Theil I. Einleitung 
zu den Beobachtungen in Pawlowsk, S. IV und V. 



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104 H- WILD ivol. ii, No. 3. J 

Als man aber hiebei ein anderes Unifilar-Magnetometer verwen- 
dete, dessen Magnet in Form und Grosse genau dem der Lloyd'schen 
Wage entsprach, fand man fur die obige Grosse die Werthe: 

0.000699 ft* 1 " e * ne Entfernung der Magnetcentren : 380 mm. 
und 0.000694 „ „ „ „ „ 580 „ 

Also selbst bei der grossern Entferaung des Ablenkungsmagnets 
erhielt man im erstern Fall noch einen um 10% unrichtigen Werth 
fur den Empfindlichkeitscoefficienten. 

Ueber die vom Beobachter zu gebenden Aufschliisse betreffend 
der Fehler beim Variometer fur Vertical-Intensitat gilt somit ganz 
dasselbe, was wir oben bei dem fur die Horizontal-Intensitat ver- 
langt haben. 

Wir haben gesehen, dass die Variometer nicht bloss zur Verfol- 
gung der Variationen der magnetischen Elemente, sondern auch zur 
Bestimmung der Fehler der absoluten Messungen nothwendig sind 
und dass fur magnetische Observatorien ein doppelter Satz von 
Variometern nicht bloss zur Wahrung der Continuitat der Beobach- 
tungen im Fall der Beschadigung eines Instrumentes und zur leich- 
tern Bestimmung der Temperatur-Coefficienten des Bifilars und der 
Lloyd'schen Wage, sondern auch fur die Ermittlung der Fehler der 
Variometer durchaus wunschenswerth ist. Als geringste Leistung 
Seitens des Beobachters zur Beurtheilung der Fehler seiner Resul- 
tate muss die Mittheilung der Resultate aller absoluten Messungen 
und der daraus abgeleiteten Normalstande beider Serien von Vario- 
metern sowie Angaben iiber die constanten Fehler der absoluten 
Messungen verlangt werden. Wer dies nicht thut, bringt sich mei- 
nes Erachtens in den Verdacht, dass von den gewohnlich bis auf 
zh 0/1 aufgefuhrten Declinations- und Inclinationswerthen schon 
die Minuten und von den Intensitaten, die man bis zu 0.000 1 ihres 
Werthes anzugeben pflegt, schon die 0.00 1 derselben fehlerhaft 
sind. 



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ON MINUTE, RAPID, PERIODIC CHANGES OF THE 
EARTH'S MAGNETISM. 1 

By Professor Max Eschenhagbn. 

In a previous communication to the Academy, a curve was ex- 
hibited which had been obtained at the Potsdam Magnetic Observ- 
atory by automatic photographic registration of the horizontal 
component of the earth's magnetic force. The striking feature of 
this curve was the fact that, in addition to the usual larger per- 
turbations, there was a series of very small waves having nearly 
the same constant period, so that these waves could, in a certain 
way, be regarded as constituting the elementary pulsations of the 
earth's magnetism. 

Since then it has been possible to obtain about sixty such 
curves. The sensitiveness of the intensity variometer was, as be- 
fore, a very high one (imm. of ordinate —0.00004 cm~* g H sec" 1 ), and 
for the time-scale a length of abscissa of 24cm. was taken to repre- 
sent one hour, hence about twelve to sixteen times that of the usual 
registration. 

All the results thus far prove that, with the means employed, it 
is actually possible to arrive at the smallest perturbations, or ele- 
mentary waves, so that a further refinement of the instrumental 
means would not promise success. 

In general, namely, the changes of the earth's magnetism take 
place gradually, so that the customary means of registration, in 
which a length of abscissa of 15mm. or 20mm. corresponds to one 
hour, suffices to reveal the phenomena, provided the curves are 
sufficiently clear and well-defined. But occasionally, on the av- 
erage about every fifth or sixth day, the usual curves present at 
certain places a partially faded or hatched appearance. A closer 
examination shows that at these times there occur very small fluctu- 
ations of short period, which, in the Potsdam Observatory, were re- 
vealed only a few hours by the rather sensitive bifilar magnetometer, 
were shown much less frequently by the unifilar magnetometer, and 
not at all by the instrument for the vertical intensity — the Lloyd 
Balance. In how far this was due to lack of instrumental sensi- 

1 Translated from the Sitzungsb. d. Preus9. Akad. d. Wi9S. zu Berlin, XXXII, 
678-486, 1897. The paper was read on June 24, 1897. 

105 



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106 M. ESCHENHAGEN [vol. 11, No. 3 ] 

tiveness on the part of the unifilar and the Lloyd Balance must 
remain undecided until the time when we shall have succeeded in 
devising instruments for the registration of the declination and the 
vertical force as sensitive as those for the registration of horizontal 
force. 

An examination of all the bifilar magnetograph traces obtained 
at Potsdam, since the beginning of 1890, shows that this phenom- 
enon consists, as we shall describe more fully later on, of a series 
of more or less regular waves of small amplitude and short period, 
and that this phenomenon occurred much less frequently in the first 
years. It is not possible to say at present whether the latter fact 
is due to the increasing of the sensitiveness of the bifilar instru- 
ment since 1894 (imm.=3.2r, instead of 5r, as before), and the em- 
ployment of a much more sensitive paper, rendering it possible to 
obtain much better defined curves than formerly, or whether it is 
due to the fact that we are approaching the years of minimum 
sun-spots. 

It is not necessary, perhaps, to state that the idea that these 
perturbations may be due, possibly, to the disturbing influence ot 
electric cars, can not be entertained, for the reason that there are 
no electric cars in Potsdam, and that those of Berlin are doubtless 
far enough away — 20 kilometers. Besides, such a disturbing influ- 
ence would make its appearance daily. 

Generally it was possible to obtain the perturbation of the hori- 
zontal force, alluded to above, with a second instrument, used as a 
control instrument, which was provided with scale and telescope, 
so that eye-readings could be made. The special intensity variom- 
eter, described in the previous communication, was set in operation, 
and it then registered the "elementary waves," whose presence, as 
stated, was revealed on the usual bifilar trace, by the partially 
faded or hatched appearance of the trace, at the time when the 
"elementary waves" were in progress. In this way it was possible 
to ascertain the time of occurrence, as well as the character of the 
phenomenon in question. It would appear thus far that these 
waves are more likely to occur during the day, and very seldom at 
rhereas in the night hours take place frequently larger, even 
*opic, waves, easily recognizable on the usual traces, their 
n period being usually several minutes, the whole phenom- 
isting rarely more* than one hour, generally much less, 
large disturbances have received special attention at the 
a Observatory since 1890, as the clearer definition of the 



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MINUTE CHANGES OF THE EARTH 'S MAGNETISM 



107 



Potsdam traces and the larger time scale employed rendered this 
more easily possible than at the other observatories. Since then 
this class of waves, or disturbances, has been subjected to a careful 
study by Dr. Arendt, of the Potsdam Observatory. He is inclined 
to deduce a relationship between them and atmospheric electric 
phenomena. 1 

The vibration period of the waves in question in this paper is 
about 30 seconds, the entire phenomenon lasting usually three to 
four hours, and occurring most frequently during the interval from 
6 A. M. to 6 P. M., or at a time when the sun is above the horizon. 
A direct influence due to solar radiation has as yet not been de- 
tected, the waves appearing equally as well on cloudy days (sky 
uniformly overcast) as on cloudless days. 

Recently, F. Kohlrausch 2 has related that he noticed, by direct 
eye-readings, on November 20, 1882, at Wurzburg, rapid changes 
of the earth's magnetism, which took place in even shorter time. 
His curve, drawn with the aid of the observed eye-readings, shows 
waves whose length, expressed in time, is on the average but 12 
seconds, whereas, as will be remembered, the average length of 
our waves, as given in the first communication, was 30 seconds. 
It is not possible to say whether both kinds of waves are to be 
referred to the same cause, since Kohlrausch's observations were 
made at a time when occurred one of the largest magnetic storms 
recorded in recent times. From November 17th to 20th the mag- 
netic needles at all the observatories on the globe were subjected 
to such violent disturbances that, in spite of the recently intro- 
duced bromide-silver paper, the trace was at times either wholly 
or partially obliterated. The storms of 1859-61 and 1870-71, 
which were possibly even more severe than the one of 1882, were 
doubtless registered even less completely, because of the less per- 
fect photographic means. 

The fact that disturbances so large and rapid as those of No- 
vember 20, 1882, should be accompanied by minute waves is cer- 
tainly highly interesting, and testifies to the importance of our 
problem — to resolve, by refinement of photographic registration, 
the earth's magnetic phenomena into its last components, or, as 
we may say, into its elements. Naturally, with such a sensitive 

1 Th. Arexdt : Beziehungen der electrischen Erscheinungen unserer Atmos- 
phare zum Erdmagnetismus. Das Wetter, Heft 11 und 12, 1896. 

2 F. Kohlrausch: Ueber sehr rasche Schwankungen des Erdmagnetismus. 
Hied. Ann. Bd. 60, No. 2, pp. 336-339. 



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108 M. ESCHBJS/HAGEN [Vol. ii, no. 3.1 

intensity variometer as ours, only disturbances of moderate range 
could be registered, so that our results and those of Kohlrausch 
are not immediately comparable. It seems, in fact, that our waves 
are typical of magnetically calm periods. This, of course, does not 
exclude the possibility that the minute waves accompanying large 
disturbances are the same as ours, only slightly modified. 

As already stated, the average length of the elementary waves 
was given in the first communication as 30 seconds. The many 
registrations obtained since slightly modify this result, and present 
another phase of this interesting phenomenon, the exposition of 
which is the chief purpose of this paper. 

It might be mentioned first, that since the end of October* 
1 896, waves shorter than 30 seconds occurred only on two days ; 
namely, November 7, 1896, and February 4, 1897. These series 
show a perfect periodicity only for short stretches, the length of 
the waves being about 12-15 seconds, and their range but half of 
that of the usual elementary wave. 

Another interesting phenomenon recorded repeatedly consists 
of wave-groups which show an analogy to tone-beats. The best 
example of this kind was recorded on February 14, 1897, between 
10 A. M. and 2 P. M. The page opposite (Fig. 1) gives a repro- 
duction of this case on the original scale. It will be seen that 
maxima and minima are clearly discernible, and divide the curve 
into groups, as aaa and bbb. The latter groups, separated from 
each other by the vertical lines, indicate the law so distinctly that 
an analysis of the phenomenon should be easily possible. 

We have before us, then, a phenomenon precisely similar to the 
one well known in acoustics; namely, the superposition of one 
wave system upon another, the vibration numbers of the two wave- 
motions differing but slightly from each other. 

Letting a x and a % equal the semi-ranges, or amplitudes, of the 
two wave motions, 7\ and T % the vibration periods, T the period of 
a tone-beat interval, we can represent algebraically the two wave- 
motions by the following well-known formulae: 

y,=a x sin jr t , y t =a t sin 7^ (/-r), 

in which t stands for a possible phase displacement. We have, be- 
sides, T l =mT f T 2 =?iT } where m and n represent the vibration 
numbers. The resulting wave is then : 

J^i+JV^i sin ?•*+** sin = £ 
Counting off the waves in Fig. 1, the value of 4:5 is obtained for 



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MINUTE CHANGES OF THE EARTH'S MAGNETISM 



109 



the ratio m:n. A single tone-beat has, on the average, a length 
of 11.4mm., corresponding to a period of 171 seconds, and hence 
71=43 and ^=34. 

For the purpose of comparison, Fig. 2 gives a graphical repre- 
sentation of the two wave-systems in which exists the relation 
m:n:: 4:5. The middle curve represents the curve resulting from 
the superposition of one of these systems on the other. It will be 
readily seen that there is a remarkable similarity between this re- 
sultant curve and the one indicated by bb in Fig. 1. The hypoth- 
esis, then, that the phenomenon is really to be ascribed to the 
combination of two wave-motions of nearly equal range and slight 
phase difference seems justifiable. 

Since the wave-groups aa in Fig. 1 have been registered much 
more frequently than the bb ones, it would appear that the ratio 
between the vibration numbers does not remain entirely constant, 
and that at times, also, a phase displacement takes place. 

There remains to be answered one objection, which can be made 
with justice ; namely, that instrumental causes — for example, the 
mechanical vibration of the needle itself — may have operated in 
the production of the waves under discussion. 

In the first communication, attention was called to the fact that 
the small magnetized steel mirror of the intensity variometer is 
strongly damped, the damping ratio being about 4, so that, with a 
period of 8 seconds, mechanical vibrations no longer come into 
question. This result will be all the surer, if we obtain the same 
phenomenon with a second and entirely differently constructed 
apparatus. Reference has already been made to the fact that the 
waves are likewise recognizable — to be sure, not with such distinct- 
ness — with the ordinary registering instrument, and also that they 
can be discerned at the eye-reading instrument, our " control bifilar," 
which we use daily in our work for the sake of comparison, the 
change of scale zero being controlled by absolute observations on 
three days in each month. While the special-intensity variome- 
ter was being set to work, eye-readings were taken at the "con- 
trol" instrument. A graphical representation suitably reduced is 
given in the upper curve of Fig. 4, while below we have in nat- 
ural size the curve as obtained by the intensity variometer. The 
accord between the curves is certainly a most satisfactory one, 
especially when we consider that the degree of sensitiveness of 
the instruments differed greatly; for the "control" instrument 
1 </.=2.7t', and for the variometer imm. of ordinate=o.4?\ The 

5 



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i io M. ESCHENHAGEN [vol. ii, no. 3.] 

latter instrument has a steel mirror of 20mm. diameter, placed at 
right angles to the magnetic meridian by imparting a proper 
amount of torsion to the quartz fibers supporting the magnet, 
whereas in the "control" instrument there is an 11 cm. long col- 
limating magnet suspended bifilarly, and damped so that its vibra- 
tion period is about 8 seconds, the damping ratio being but 2.6. 
The difference in the construction of the two instruments could 
therefore hardly be greater. The accord between the two has more- 
over been proven in another connection by direct observations 1 
made every 5 seconds. 

In order to show again that the law pervading the wave motions 
bb y in Fig. 3 is the result of external forces only, an endeavor was 
made to obtain these waves in some artificial manner. 

Let us take a short magnet — for example, a piece of a magnetized 
knitting-needle 4 cm. long— and place it horizontally in the mag- 
netic meridian at a distance of 1.5m. from the steel mirror placed 
perpendicularly to the meridian. The small steel magnet at the dis- 
tance given will be deflected 3-4 minutes of arc, a quantity which 
represents on the curve about the same number of millimeters. If 
we place the small magnet vertically, and at the same height as 
the steel mirror, we obtain no deflection. As we turn the small 
magnet back, however, into its primary, horizontal position, the 
angular deflection will continue to increase until the maximum 
value given above is reached. Since the effective magnetic mo- 
ment is proportional to the cosine of the inclination of the needle, 
or to the sine of the co-inclination, the law of increase of angular 
deflection would be the sine law, such as we have graphical repre- 
sentations of in the upper and lower curves of Fig. 2. The interac- 
tion of two such magnets, which lie either beside each other or 
above one another, would vary of course with their relative posi 
tion, sometimes a summation of effects, at other times a counterbal- 
ancing would occur. A simple apparatus was next constructed, con- 
sisting of two drums, whose diameters were 4 and 5 cm., respectively, 
and the two were connected by an endless cord. To the drums 
were next fastened the small magnets, whose moments were about 
equal, for example, 16 and t8 cmgr. units, and which were 1.76 
meters distant from the needle of the magnetometer. As the drums 
were revolved, the magnets assumed successively the positions corre- 
sponding to those of the two wave motions. With the hand, one drum 

'M. Eschenhagen: Ueber Simultan-Beobachtungen erdmagnetischer Varia- 
tionen, Terrestrial Magnetism , Vol. 1, p. 59, 1896. 



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1 12 M ESCHENHAGEN [Vol. ii, no 3 j 

was turned out of the initial position, in which both magnets were 
parallel and vertical, and revolved completely once in 40 seconds, 
according to the beat of a chronometer. The other drum then made 
the complete revolution in 32 seconds, and the registering appa- 
ratus recorded the wave groups indicated by the vertical lines in . 
Pig- 3 ; whereas the earth's magnetic force proceeded gradually, as 
will be seen from the parts of the curve, Fig. 3, before and after the 
wave groups. The indisputable similarity between these waves 
and those of Fig. 1 proves that the needle is subjected continuously 
to external influences, so that we are justified in drawing the 
conclusion that there actually occur in nature at times similar period- 
ically increasing and decreasing forces whigh affect the earth's mag- 
netism, and which occasionally, by superposition, produce a phe- 
nomenon similar to that of tone beats. The following data will give 
us the magnitude of these forces. From the maximum range, 
6mm., of the waves bb, (Fig. 1,) we find the ranges of the wave sys- 
tems, taking them as equal, to be 3mm., which corresponds to a 
change of the horizontal component of the earth's magnetic force 
of i.2r=o.ooooi2 cm." H ^ sec." 1 

Of special importance is the question as to the local distribu- 
tion of these elementary waves, with regard to which, to be sure, 
but few investigations are at hand. 

In 1895, in conformity with an agreement between Herr Stuck, 
of the Wilhelmshaven Observatory, and myself, magnetic observa- 
tions were made by us every five seconds, at precisely the same 
times, and at stated hours. Other observatories followed, and 
in 1896 fifteen observatories took part, there being four of 
these "term" hours. These observatories were distributed over 
the globe, though not uniformly. The first intention of these 
observations was to ascertain as accurately as possible the sim- 
ultaneity in occurrence of the larger magnetic disturbances, over 
widely distributed areas, a fact already made very probable by the 
old observations of the Magnetic Association. In this way was 
obtained at the same time material for our present purpose. 

The results obtained thus far show that large disturbances suf- 
fer from place to place not inconsiderable modifications. 1 With re- 
gard to the small waves in question here, no general result can as 

1 A more detailed account will appear later, viz., in Veroffextlichunoen des K. 
Meteorolgischen Instituts : Ergebnisse der Magnetischen Beobachtungen in 
Potsdam^ Anhang, 1896. 



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MINUTE CHANGES OF THE EARTH 'S MAGNETISM X17i 

yet be deduced, as the instruments employed at the various observ- 
atories differed too greatly in the matter of sensitiveness. 

From the 1895 observations, however, especially those from May 
1 8th to June nth, it can be seen that at Potsdam and Wilhelms- 
haven, there were a few series of elementary waves, which within 
the limit of the observing error (1-2 seconds) occurred simultane- 
ously. In a paper written at that time, 1 it is mentioned that, in the 
course of an hour, about 120 turning points were observed at both 
places. The curves, exhibited before the meeting of the Deutsche 
Naturforscher at Liibeck, reveal waves of 40-50 seconds in length, 
which were shown up strikingly at both places. On account of the 
want of proper registration means at that time, itwas not possible 
to recognize that we really had before us the smallest changes of the 
earth's magnetism. 

From this it would appear that these elementary waves may 
occur simultaneously, within one second or a few seconds, over a 
somewhat large area ; but a final conclusion will only be possible 
when ^ye have before us simultaneous registrations from more places. 
The decision reached by the directors of meteorological institutes 
at their meeting in Paris, 1896, will doubtless assist in bringing 
about, soon, international cooperation in these investigations. When 
we have drawn the final conclusion, then first can we approach 
the question as to the origin of these waves with some degree of 
success. At present we can only speculate. 

Recalling that, according to the investigations of Schuster 2 and 
von Bezold, 8 we must refer the origin of the large diurnal waves to the 
highest layers of the atmosphere, it may be permissible to surmise 
that these smallest waves likewise have their rise in this region, if 
special solar phenomena are not the primary cause. As these waves 
proceed through the air, they may be modified by the sun's rays 
in a manner similar to that in the case of electric discharges. Fur- 
thermore, the conductivity will be very different for those currents 
induced in the earth, which currents in turn again influence our 
needles, and in this way may it be possible to explain the change 
in the vibration number of the second wave system. Finally it 
will be of importance to investigate whether the distribution of 
electric waves passing into different media can cause such a slowing 

1 Terrestrial Magnetism, Vol. I, pp. 55-61. 
» Phil. Trans. R. 5., Vol. 180, A. pp. 467-518, 1889. 

•ZurTheorie des Erdmagnetismua, Sitzber. d. Pr. Akad. d. Wiss. zu Berlin, 
xviii, 1897. 



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ii 4 M - &TCHENHAGEN (vol. ix. no. 3. 

up of the period as is actually found. There remains the possibil- 
ity of assuming that magnetic effects are produced in a manner 
similar to that of Rontgen's; 1 namely, by various displacements 
of the dielectrically polarized atmosphere with reference to the 
earth's surface and the highest conducting layers of the air. 

As an aid in observing rapid and small changes of the earth's 
magnetism, the use of large wire-spools might recommend itself— 
a suggestion which I have already made some time since. 2 As is 
well known, Dr. Giese had already measured, in 1883, at the German 
polar station, Kingua-Fiord, the induction of the earth's magnet- 
ism in a large plane circuit, embracing about 8 square kilometers, 
the method used being that suggested by Werner von Siemens. 
He found that the currents ran parallel to the changes of the earth's 
magnetic vertical force, and hence were directly proportional to 
these changes, and inversely proportional to the corresponding time 
interval. This shows that the method is especially sensitive for 
the purpose of measuring very rapid and small changes of the 
earth's magnetism. 

If we use, in place of the large circuit, a large wire-spool of 
sufficient winding area, we shall likewise obtain, with a sufficiently 
sensitive galvanometer, induction effects from the earth's magnet- 
ism, and have the advantage besides of being able to place such a 
spool in the direction of the various components, or of the total 
force of the earth's magnetism. The slow diurnal magnetic changes 
do not enter any longer into account, and the galvanometer will 
reveal best the most rapid changes. In this way we obtain an in- 
strument which operates like the galvanometers which are used in 
the measurement of telluric currents, and which likewise respond 
best to the rapid changes of the earth current. 

1 Electrodynamische Wirkung bewegter Dielectrica. Sitzungsber. d. Pr. Akad. 
zu Berlin, 1888, pp. 23-28. 

* Internationale Polar Forschung, 1882-83. Ergebnisse der deutschen 
Stationen. Bd. I., Kingua-Fiord, pp. 597 and 598, Berlin, 1886. 



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LETTERS TO EDITOR 



"THE NON-CYCUC EFFECT" UND "DIE ERDMAGNETISCHE 
NACHSTORUNG." 

With reference to Dr. van Bemmelen's remarks under the above head, 
in your last number, may I briefly state my point of view? My first 
paper 1 dealt with the declination and horizontal force results at Kew dur- 
ing the selected quiet days of the five years, 1890-4. The " non-cyclic " 
effect was only one of a variety of subjects dealt with, and was considered 
mainly from the point of view of its influence on the declination and 
horizontal force inequalities, etc. When preparing that paper, I simul- 
taneously worked up the corresponding vertical force and inclination 
data ; but feeling doubt in their case as to the sufficiency of the temper- 
ature correction, held them over pending further inquiry. That inquiry 
did not encourage me to publish inequality and similar results last year, 
but inasmuch as no appreciable temperature uncertainty affected the 
4t non-cyclic " results, either in vertical force or inclination, it seemed a 
pity to further defer their publication. Also, a year having elapsed since 
the publication of the first paper, I decided to utilize its results, and pub- 
lish particulars of the " non-cyclic" effect in all the elements during the 
six years, 1890-5. This is all explicitly stated in the second paper. 2 

The " quiet " days employed at Kew are those selected by the As- 
tronomer Royal, who takes five days each month, the principle of selec- 
tion having, as I understand, nothing to do with the time interval to or 
from a magnetic disturbance. Of the five " quiet " days, it is compara- 
tively seldom that even two are consecutive, the character of the days 
preceding and succeeding the selected days being variable. Dr. van Bem- 
melen, on the contrary, approached the subject from the side of the mag- 
netic disturbance, arid selected his quiet days with reference to it. The 
two sets of days being so largely different, it is surely obvious that, for 
my purpose, Dr. van Bemmelen's data — even if his investigations had ex- 
tended to Kew — however interesting in themselves, would have been of 
use only in a general and subsidiary way. 

As to my reference to Dr. van Bemmelen's work, though called by 
him a " fluchtigen Beriihrung," it occupies some ten lines of text in a 
short paper of eight pages, and gives an explicit reference to the Meteor- 
ologische Zeitschrift for September, 1895. The words " theoretical con- 
clusions " were used in their ordinary neutral sense, and were not in- 

1 B. A. Report, 1895, p. 209 ; reviewed in Terrestrial Magnetism, Vol. I, p. 95. 
*B. A. Report, 1896, p. 231 ; reviewed in Terrestrial Magnetism, Vol. II, p. 77. 

"5 



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u6 C. CHREE [vol. ii, no. 3.] 

tended to imply either exuberance of imagination or paucity of facts. 
In my first paper, I had been led to regard a diurnal variation in the 
non-cyclic effect as probable, reasoning from certain phenomena of mag- 
netic storms described by Sabine and Lloyd, and Dr. van Bemmelen's 
independent investigations put this conclusion, as I explicitly said, on a 
much securer basis. To emphasize the value of Dr. van Bemmelen's 
paper, I mentioned that his data were derived from a variety of stations, 
and that they encouraged the belief that the non-cyclic phenomena 
might throw a valuable light on the general theory of terrestrial mag- 
netism, and not merely on the phenomena of " quiet " days. I suggested 
the expediency, in the meantime, of not committing one's self to the 
view that the connection between the " quiet " day phenomena and mag- 
netic storms must necessarily be solely one of direct cause and effect. 
In justice to myself, I should mention that my investigations were hardly 
so parochial as Dr. van Bemmelen's remarks suggest ; for, as stated in 
my first paper, I assured myself that the " quiet " day results at Green- 
wich and Falmouth showed the same general features as at Kew. 

One other aspect of the case I should like to refer to, as it not only 
largely influenced the form and scope of my paper, but still remains a 
matter of considerable importance to at least two English observatories. 
The " quiet " day system in operation at Greenwich, Falmouth, and Kew, 
was adopted largely on the initiative of members of the B. A. Magnetic 
Committee, and mainly with the view of securing the co-operation of 
observatories which, in the absence of State aid, were unable to tabulate 
all the curves. When the scheme was adopted, such a phenomenon as 
the non-cyclic effect was apparently unsuspected, and, in my opinion, it 
was desirable to indicate concisely to the Committee the several ways 
in which this effect influences, or is likely to influence, magnetic tables 
based on the selected " quiet " days alone. 

Before concluding, I wish to acknowledge, as fully and heartily as 
Dr. van Bemmelen, that our original papers on the subject were quite 
independent, and I can assure him of my desire to do full justice, not 
merely to his past work, but to the further good work we may hope from 
him in the future. Charles Chree. 

Kew Observatory, July 28, 1897. 



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LETTERS TO EDITOR 



"7 



SUR L'INCLINAISON DE V AIGUILLE AIMANffeE X L'fePOQUE 

ETRUSQUE. 

Les premieres observations directes de l'inclinaison de l'aiguille 
aimantee datent de la fin du XVI« siecle ; des informations ant£rieures 
pouvaient e*tre tirees de la position du point de convergence des rayons 
de l'aurore boreale, si cet element avait £t£ observe au moyen-age. 

Dernierement M. Folgheraiter a public sur le meme sujet plusieurs 
notes interessantes, dont M. Chistoni a fait une analyse dans le numero 
2, tome II, de ce journal. En se reportant a l'aimantation conserved par 
certains objets d'argile cuite, 1' Auteur est arrive* a ce resultat, que l'in- 
clinaison en Italie a l'epoque £trusque, au VIII C et VI e siecles avant 
notre ere, a 6te" nulle ou meme negative. 

Ce resultat surprenant m'a engage a faire une investigation theorique 
sur la valeur probable de l'inclinaison a cette epoque Sloignee ; je me 
permets d'en communiquer ici les resultats, sous toutes les reserves 
qu'impose l'£tat encore provisoire de la theorie. 

Dans un Memoire public dans le tome V des Annales de l'observa- 
toire de Stockholm, j'ai £tudie" les variations de la fonction des forces 
magn€tiques d'apres l'ensemble des observations recueillies pendant les 
quatre derniers sifccles ; il semble en resulter pour la fonction des forces 
a une epoque quelconque, une expression analytique tres simple, qui 
consiste en une sSrie de termes de la forme 

/*? a* cos n (w+y'* +w ( J /) , 

P*2 designant une fonction sph£rique d'ordre i, « la longitude, tf ( J, /* et 
m { H des constantes. Les dSrivees de cette fonction prises par rapport 
aux axes coordonnees representent les composantes de la force. 

Si Ton demande les valeurs extremes de l'inclinaison magn£tique, le 
temps /, ou a lieu le maximum ou le minimum, est donne* par la condi- 
tion 2t=o, ou si Ton se repute a l'expression de i, 

les composantes de la force X y K, et Z €tant de la forme precitee. C'est 
une equation transcendante tres compliquee, qui resout completement la 
question. Or, vu la connaissance encore imparfaite, que nous avons des 
constantes num£riques qui entrent dans les formules, je me suis borne" a 
calculer prealablement, pour un cycle complet, correspondant a une revo- 
lution du moment magn£tique principal de la Terre, la valeur de l'in- 
clinaison magn€tique en Italie, et particulierement pour Rome. 

En se bornant aux termes des trois premiers ordres, dont les mouve- 
ments sont seuls connus avec quelque precision, on a trouve" le resultat 
suivant. 

6 



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La figure ci-jointe donne une representation graphique de ces nom- 
bres. La courbe met en Evidence le grand cycle de trois mille annees, 
auxquelles s'ajoute une se'rie d'oscillations plus faibles, dont les pe'riodes 
varient de treize cents k quatre cents annees. Le maximum d'inclinai- 
son d'environ 75°>£, a eu lieu au treizieme siecle. Un minimum a eu lieu 
au huitieme siecle avant notre £re ; or, comme ce minimum ne descend 
pas au-dessous de 48°^, il parait peu probable que l'inclinaison en Italie 
ait pu jamais s'abaisser jusqu' a la valeur ze*ro ou m£me au-dessous. 



+70° 



+6o° 



+50° 



+40 



av. J. C 


—500 


+500 +1000 


+1500 +200C 


























v- 


y 










■ %y 













Nous ne voulons guere revendiquer une valeur absolue pour ces re*- 
sultats, dont les fon dements numeYiques sont d^duits d' a peine quatre 
cents annees d'observations. N€anmoins, grace aux idees theoriques que 
nous nous sorames formees sur la cause des variations, on peut supposer 
qu'ils repre*sentent, au moins dans ses traits ge'ne'raux, la marche des va- 
riations. [La theorie vient ainsi jeter des doutes sur l'exactitude des r£- 
sultats tir£s de Texamen des objets e'trusques. Toutefois, la me'thode 
de M. Folgheraiter est extr£mement intSressante, et avant de se pro- 
noncer positivement sur la question, il y aurait lieu de Tappliquer a 
d'autres objets provenant d'endroits diffe*rents. C'est dans tous les cas, 
une £tude attrayante, qui peut £tre vivement recommandee aux archae- 
ologues et aux physiciens.] 

Observatoire de Stockholm V. Carlheim — Gyllenskold. 



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LETTERS TO EDITOR 



119 



RESULTS OF MAGNETIC OBSERVATIONS AT THE OBSERVA- 
TORY INFANT D. LUIZ (LISBON), i890-'96. 

J'ai l'honneur de vous remettre un risumi des observations magne*t- 
iques dans Tobservatoire du Infant D. Luiz a Lisbonne de 1890 a 1896. 

Les observations sont directes, et des 5 selected days, afin de les com- 
parer ensemble. 

Les observations absolues de la declinaison sont faites 3 fois par mois, 
et celles (1) — i*£ sont d^duites des courbes du declinographe de tous 
les jours. 

Les observations de la force horizon tale {H) sont faites une fois par 
mois, et celle de l'inclinaison 3 fois par mois. 

Les differences entre les observations directes et les 5 selected days, 
sont tres petites. 



Year. 



1 gj i 

Declination 1 jj-g I Inclination* I 

I > i 



Force in C. G. S. units. 



I Direct observation 

1890 5 selected days, . 

Direct observation, 

1 891 15 selected days, . 

Direct observation, 

1892 5 selected days, . 
i 
I Direct observation, 

J 893 15 selected days, . 

Direct observation 
1894 5 selected days, 

I Direct observation 
J 895 5 selected days, . 

'Direct observation, 
1896 5 selected days, . 



I 



Hori'tai* Vertical. 



18 
18 



5.&> 

5.27 



571 
5-77- 



18 0.23 I 7.09 

17 59.24 7.62 

17 54.26 8.13I 

17 5340 8V 

17 4938 9-io| 

17 48.50 8.91, 

I I 

17 44.67 8.38! 

17 4366 8.34 

17 39-So 74 2 

17 3909 752 



I 



5»° 3'-&> 

58 32.38 

58 30.81 

58 31-37 

58 28.35 

58 29.42 

58 24.63 

58 23.06 

58 21.51 

58 21.43 

58 1566 

58 1566 



Total. 



O.23155 0.37817, O.44343 



O.23155 

O.23172 
O.23178 



0.37844! O.44366 

0.37835: O.44367 
0.37857 O.44389 



O.23178 O.37795 O.44336 



O.23192J O.3783I 

O.23270' O.37820 
O.23277 



17 3593 , 6.86' 
17 35-10 ! 7-53 



58 
58 



11.81 
12.12 



0.37837 

0.37801 
0.37827 

o.3773i 
o.3775i 

.. 0.37648 
0.23358 1 0.37676 



0.23302 
0.23310 

0.23344 
0.23351 

0.23346 



0.44360 

0.44405 
0.44426 

0.44406 
0.44432 

o.44374 
0.44389 

0.44299 
0.44329 



1 8a+2p of the declinograph register. 

t 

8 3 observations each month. 
Lisbonne, 6, Aout, 1897. 



2 2p— -8a in each day. 

* 1 observation each month. 
J. Capello. 



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LIST OF PUBLISHED PAPERS ON TERRES- 
TRIAL MAGNETISM AND METEOR- 
OLOGY BY THE LATE CHARLES 
CHAMBERS] F. R. S. 

Compiled by Professor N. A. Moos, Director of Government Observ- 
atory, Col aba, Bombay, and by L. A. Bauer. 



A. — Papers Discussed and Published under the Authority of Gov- 
ernment. 

On the solar variations of magnetic declination at Bombay. Phil. Trans., 
1869, pp. 363-386. 

The absolute direction and intensity of the earth's magnetic force at Bombay. 
Phil. Trans., 1872, pp. 75-90. 

The normal winds of Bombay. Appendix I to Bombay Magnetical and Me- 
teorological Observations, 1865-70, pp. 199-212, Bombay, 1872. 

On the lunar variations of magnetic declination at Bombay. Appendix III 
to Bombay Magnetical and Meteorological Observations, 1865-70, pp. 
235-242, Bombay, 1872. 

Meteorology of the Bombay Presidency. 1 vol. 4 , pp. 1 to 295, and 1 portfolio 
of 82 diagrams, etc. Eyre and Spottiswoode, London, 1878. 

Notes on a comparison of two unifilar magnetometers, and on magnetic in- 
duction as affecting observations of the intensity of the horizontal mag- 
netic force. Appendix to Bombay Magnetical and Meteorological Ob- 
servations, 1871-78, pp. [53H60], Bombay, 1881. 

Bombay Magnetical and Meteorological Observations, 1864 to 1894. Introduc- 
tions and Compilations, 14 vols. 4 , Bombay, 1 867-1895. 

Appendices to Bombay Magnetical and Meteorological Observations, 1879-82, 
1 vol. 4 . . 

I. History of the set of magnetographs established at the Col&ba Ob- 

servatory, with a new theory of the vertical force magnetometer, 
pp. [1] to [83]. 

II. On the solar and lunar variations of magnetic declination at Bombay 

in the years 1846-1872, pp. [84] to [137]. 

III. On the solar and lunar variations of the earth's magnetic force at 

Bombay in the years 1847-1872, pp. [138] to [193]. 

IV. The solar diurnal variations of declination, horizontal force, and 

vertical force at Bombay, as derived from the registrations of the 
Col&ba magnetographs, pp. [194] to [235]. 

V. Influence of height above or below the ground level upon the di- 

urnal variations of declination and horizontal force, pp. [236] 
to [241]. 

l Cf. Vol. I, p. 155, this journal. 
120 



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LIST OF PUBLISHED PAPERS 121 

Diurnal variations of declination and of horizontal force for each month 
(and year) of the years 1865 to 1872, deduced from the readings of Grubb's 
declination magnetometer and of Grubb's horizontal force magnetometer. 
Appendix to Bombay Magnetical and Meteorological Observations, 1884, 
pp. [1] to [16]. 

Appendices to Bombay Magnetical and Meteorological Observations, 1886. 

I. On the luni-solar variations of magnetic declination and horizontal 

force at Bombay, and of declination at Trevandrum. 

II. Luni-solar variations of magnetic declination at Batavia, and refer- 

ences to later extensions of the investigations of the preceding 
paper. 

IIL On the influence of temperature upon the bifilar magnetometer. 

IV. Effect of heating the magnetograph room on the scale-coefficient 

of the vertical force magnetograph. 

V. Temperature coefficient of the vertical force magnetograph. 

VI. Temperature coefficient of the horizontal force magnetograph. 
Appendices to Bombay Magnetical and Meteorological Observations, 1888-89, 

1 vol. 4 . 

I. History of the set of magnetographs established at the Col&ba Ob- 

servatory, Bombay. 

II. The solar diurnal variations of declination, horizontal force, and 

vertical force at Bombay, as derived from the registrations of 
the Col&ba Magnetographs [continued]. 

Appendix to Bombay Magnetical and Meteorological Observations, 1890. 

The absolute magnetic declination and horizontal force at Bombay, and 
their secular and annual variations. 

Appendix to Bombay Magnetical and Meteorological Observations, 1891-92, 
1 vol. 4 . 

The secular variation of magnetic dip at Bombay during the years 
1867 to 1892. 

B.— Papers Published by Learned Societies. 

On the direct influence of a distant luminary upon the diurnal variations of the 
magnetic force at the earth's surface. Phil. Mag. March, 1858. 

On the nature of the sun's magnetic action upon the earth. Proc. Roy. Soc, 
vol. 12, 1862-63, p. 567. 

On the nature of the sun's magnetic action upon the earth. Phil. Trans. 
R. S., 1863, pp. 503-16. Declination disturbances at Bombay, 1866. Proc. 
Roy. Soc, vol. 15, 1867, pp. 111-114. 

On the uneliminated instrumental error in the observations of magnetic dip. 
Proc. R. S., vol. 17, 1868-69, p 427. 

On the solar and lunar variations of magnetic declination at Bombay. Part 1. 
Proc Roy. Soc, vol. 17, 1869, pp. 161, 162. 

Observations of the absolute direction and intensity of terrestrial magnetism 
at Bombay. Proc. Roy. Soc, vol. 17, 1869, pp. 426, 427. 

On the lunar variation of magnetic declination at Bombay. Proc. R. S., vol. 
2°» P- *35» Abstract 

Absolute direction and intensity of the earth's magnetic force at Bombay and 
its secular and annual variations. Proc R. S., vol. 20, p. 107, Abstract, Phil. 
Trans., 1876, pp. 75~90- 



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I2 2 LIST OF PUBLISHED PAPERS [vol. ii, no. 5.] 

On the lunar variations of magnetic declination at Bombay. Proc. Roy. Soc, 
vol. 20, 1872, pp. 135, 136. 

On magnetic induction as affecting observations of the intensity of the hori- 
zontal component of the earth's magnetic force. B. A. A. S. Rep., 1877, 
PP- 33» 34. 

Sun-spots and terrestrial phenomena. I. On the variation of the daily range 
of atmospheric temperature, as recorded at the Col&ba Observatory, 
Bombay. II. On the variation of the daily range of the magnetic decli- 
nation, as recorded at the Col&ba Observatory, Bombay. Roy. Soc. 
Proc, vol. 34, pp. 231-264. 

Examples of the application of a modified form of Sabine's method of re- 
duction of hourly observations of magnetic declination and horizontal 
force to a single quarter's registrations of magnetographsat the Col&ba 
Observatory, Bombay, to accompany the Second Report of the Committee 
appointed for the purpose of Considering the best means of Comparing 
and Reducing Magnetic Observations. Published with the British Asso- 
ciation Report for 1886. 

Luni-solar variation of the vertical magnetic force at Bombay for the single 
quarter, November, 1875 to January, 1876, to accompany the Third Report 
of the Committee appointed for the purpose of Considering the test 
means of Comparing and Reducing Magnetic Observations. Published 
with the British Association Report for 1887. 

By C. and P. Chambers. On the mathematical expression of observations of 
complex periodical phenomena, and planetary influence ou the earth's 
magnetism. Phil. Trans., vol. 165, pp. 361-402. 

On the luni-solar variations of magnetic declination and horizontal force at 
Bombay, and of declination at Trevandrum. Proc. Roy. Soc, vol. 40, 1886, 
p. 316. 

On the luni-solar variations of magnetic declinatiion and horizontal force at 
Bombay, and of declination at Trevandrum. Phi!. Trans. Roy. Soc, 1887, 
vol. 178, A. 



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AGONIC CURVE OF NORTH AMERICA 



123 



SECULAR VARIATION IN THE POSITION OP THE AGONIC CURVE 

OF NORTH AMERICA BETWEEN A. D. 1700 AND 1900, 

ACCORDING TO C. A. SCHOTT. 




[Above plate loaned by Maryland Geological Survey.] 



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124 



L. A. BAUER 



[Vol. II, No. 3.) 




[The diagram above exhibits at a glance all the characteristic features of the 
secular variation of the magnetic declination in the Northern Hemisphere. The 
stations selected are typical of the regions represented by them, and, as will be 
seen, encircle the globe. The data has been taken from various sources. The plate 
has been loaned by the Maryland Geological Survey.—!,. A* B.] 



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Terrestrial Magnetism, December, 18^, 



, + 



ELECTRIC CAR DISTURBANCES AT THE MAGNETIC 

OBSERVATORY OF THE UNITED STATES NAVAL 

OBSERVATORY. 

By Commander C. H. Davis, U. S. N., Superintendent of Naval 

Observatory. 

The magnetic instruments at the Naval Observatory in the city 
of Washington consist of a Kew vertical-force needle, Kew declina- 
tion needle, Kew horizontal-force needle, and Mascart .vertical-force 
needle. Therte instruments are mounted underground, in a vault 
specially designed for the purpose, and are self-registering by means 
of photography. 

The Observatory itself is situated on Georgetown Heights in 
the suburbs of the city of Washington, on a spot selected by a 
commission appointed for the purpose.. The purchase of this site, 
which is irregular in shape, and contains nearly seventy acres, was 
made in 1882. One of the principal requirements of the commis- 
sion was to choose a site which should probably remain free from 
disturbances due to the proximity of a city and the effects of traffic. 
The electric railway had not then been perfected, and no more de- 
sirable site could have been selected. The construction of the new 
buildings, laying out and grading the grounds, and preparing lor 
the removal of the instruments extended over a period of ten years, 
and the old site of the Observatory on the bank of the Potomac 
was finally abandoned in 1893. 

The magnetic instruments as above described were mounted in 
January, 1894. There are two lines of electric railway passing on 
parallel lines in a northwesterly direction on either side of the Ob- 
servatory grounds ; the Georgetown and Tennallytown Road, with 
branches which extend to distances of from seven to eight miles 
from the terminus in Georgetown, the main line passing within 
1,400 feet of the magnetic observatory, being the nearest, to the 
west. The other road runs from Washington to Chevy Chase, pass- 
ing the Observatory to the east at a distance of three-fourths of 
a mile. 

3 125 



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126 C. H. DAVIS [vol. ii. No. 4 J 

When the instruments were mounted it was immediately no- 
ticed that there was a disturbance of the vertical force trace during 
the hours when the cars were running on the Georgetown and Ten- 
nallytown Road. This disturbance was not at first sufficiently se- 
rious to destroy the value of the observations. It was apparent in 
a widening and blurring of the line (trace), and the question was 
raised as to whether the disturbance was mechanical, and an experi- 
ment was undertaken to determine this, with a negative result. 
The disturbance remained about the same until the spring of 1897 
when it gradually assumed larger proportions and began to show 
itself also in the horizontal force and declination, the increase in 
disturbance being attendant upon a very heavy increase in the 
traffic of the road. It became evident that the effect of currents 
from the road operated not only to blur the trace but to increase 
the vertical force. Magnetic values are published to the millionth 
of a dyne, and it has been found that a single car running on the 
Glen Echo branch of the Tennallytown Road increases the vertical 
force 0.000075 dynes. It would often occur during the months of 
July and August, when summer travel on this branch was heavy, 
that the vertical force would be increased three or four hundred 
millionths of a dyne for hours at a time. The effect however is 
sometimes to decrease the vertical force. On August 3, 1897, the 
vertical force decreased 0.001500 dynes, fluctuated about the new 
value for an hour and a half and then returned to about the former 
value. Such sharp changes as these are due to the trolley wire 
breaking and shortcircuiting the line. The effect on the elements 
which this may have depends on engineering details with which it 
would be difficult for an outsider to become acquainted. During 
the past month the Georgetown and Tennallytown Road "bonded" 
its line ; that is, it completed metallic contact between the ends of 
its rails and connected these with the system of water mains in the 
city of Georgetown with the view of establishing a free metallic 
return for its grounded current. This has had no perceptible effect 
in diminishing the disturbance at the Observatory. 

With a view to determine whether most of the effect on the 
needles might not be due to currents transmitted by the gas and 
water pipes which supply the magnetic observatory building, one 
of the two vertical force instruments was mounted in a temporary 
structure about four hundred feet from all such pipes, and also 
about four hundred feet more remote from the railroad than the 
Observatory building itself. The disturbance in this situation 
proved little if any less. 



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ELECTRIC CAR DISTURBANCES 127 

The disturbances so far noticed have been traced directly to the 
nearest road, the Georgetown and Tennallytown ; but were traffic 
on this road to cease the Observatory would still be within the 
radius of influence of the Washington and Chevy Chase Road 
three-fourths of a mile distant, the effects of which are obliterated 
in the preponderating influence of the closer road. Experiments 
conducted last summer, at the Magnetic Observatory of Toronto, 
which is the only other magnetic observatory in North America, 
and which is unfortunately in a worse predicament than this Ob- 
servatory, the trolley road passing within 700 feet, demonstrated 
that magnetic instruments must be removed to a distance of at least 
two miles before the disturbances of an electric railway cease to be 
apparent. Observations at Toronto have been discontinued. 

In addition to the disturbances which can be traced to the elec- 
tric railway there are during the night hours, at more or less reg- 
ular times, small disturbances which are probably due to throwing 
off the current in arc-light circuits in the city, these circuits having 
a grounded return wire. 

It thus appears that the use of powerful electric currents for 
commercial purposes has destroyed the usefulness of the only two 
magnetic observatories on the North American continent. That is, 
considerations of gain so far outweigh considerations of science 
and knowledge that the latter do not enter where questions of 
money prevail. This presents the commercial aspect of the ques- 
tion on which it would be out of place to expatiate. A remedy 
might be obtained by legislation, and that remedy could possibly 
be reached by making it evident that the grounding of powerful 
electrical currents is either wasteful and extravagant or is working 
an injury to other commercial enterprises. The remedy, if reached 
at all, will be reached when the question becomes one of money on 
both sides. 



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t- 



ELSTER AND GEITEL'S RESUME OF RECENT PAPERS 
ON ATMOSPHERIC ELECTRICITY. 1 

By Alexander McAdie. 

In this supplement to the Year-book of the Ducal Gymnasium 
at Wolfenbiittel for 1897, Professors Elster and Geitel sum up in 
twenty-four closely printed pages the chief results of the more 
recent investigations in atmospheric electricity. Few are more 
competent to undertake such a task. While there has been con- 
siderable activity displayed in many parts of the world lately in 
connection with atmospheric electricity, probably nowhere has this 
activity been more marked than at Wolfenbiittel. We do not for- 
get the work of Professor F. Exner, the occasional papers of Lord 
Kelvin and his co-workers, and the contributions of Schuster, Chree, 
Andr£e, and others. Yet for systematic and comprehensive con- 
tributions to our knowledge or" atmospheric electricity, we must 
give the larger measure of praise to Professors Elster and Geitel. 
For some years they have pointed out the proper lines of inquiry, 
and at the same time have described new methods of observation. 
Previous to their publication, in 1893, of a Report embracing the 
period from i860 (when Lord Kelvin gave the subject a great im- 
petus) to 1892, it was not easy to find a good compendium of the 
subject. New contributions were scattered, naturally enough, in 
different journals and reports of scientific bodies, and as for man- 
uals of Physics and Meteorolgy, it was but too true, as our authors 
state, for one to find in these, references only to the work of Frank- 
lin, Volta, and perhaps Dellman. 

Referring to their publication of 1893, l ^ e authors state that 
many views then thought to be well established, are now in doubt. 
In the present paper they seek to present the newest results, lay- 
ing stress upon facts rather than theories. The whole subject is 
treated under three heads : First, the static phenomena connected 
with water vapor; second, electrical disturbances accompanying 
precipitation ; and third, discharges. Naturally, the divisions are 
not sharply marked. At the end of the paper, the known facts in 
atmospheric electricity are classified as follows : First, those deal- 

1 Zusatnmenstellung der Ergebnisse neurer Arbeiten iiber atmospharische Elec- 
tricitat. Von J. Elster und H. Geitel. Wissenschaftliche Beilage zum Jahres- 
bericht dfs Herzoglichen Gymnasiums zu Wolfe nbult el y 1897. Progr. No. 726. 
Wolfenbiittel, 1897. 21x25 cm. Pp.24. 

128 



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A TMOSPHERIC ELECTRICITY 1 29 

ing with the electrical field above the precipitation level and its 
variations ; second, those associated with precipitation ; and third, 
auroral displays and similar appearances. The important question 
of how the earth and atmosphere acquire an electrical charge is 
discussed at length ; but it must still remain a matter of conjecture 
whether the earth as a planet has a given negative charge, or 
whether the free positive electricity of the atmosphere belongs to 
the lower air strata. Some hold that the seat of the complementary 
charge of the earth is at a very great distance from us. But 
further experimentation is necessary to account for the great varia- 
bility of the potential, not alone in the irregular perturbations, but 
also in the daily and yearly periods. Omitting days of rain and 
snow, it would appear that in the temperate zones the mean daily 
value of the potential is higher in winter than in summer ; and 
there is also a plainly marked diurnal variation. There are no 
simultaneous changes as in magnetic disturbances. If observations 
were made in calm, clear weather, beyond the influence of smoky, 
dusty cities, with stations not more than 100 metres apart, it would 
be Jound that the mean values ol observations of about five minutes 
duration would agree closely. Our authors infer that the cause of 
the variation is to be found in the lower air strata. To determine 
the cause of the daily and yearly period, observations should be 
made on the highest mountain peaks. Our authors refer to the 
observations made for them by Peter Lechner at the Sonnblick, 
3,000 metres above sea level, from which it would seem that the 
daily and yearly variability is less in clear weather at this height 
than in the lowlands. The daily mean appears to be independent 
of the time of the year. Observations made at the summit of 
Dodabetta, in India, and on the Eiffel Tower confirm this view that 
the potential becomes less variable with increasing height. Obser- 
vations of the potential in the free air are of the greatest impor- 
tance. Reference is made to the experiments of Exner and Tuma, 
near Vienna, and the contradictory experiments with the balloon 
Phoenix at Charlottenburg. 

The views of Ekholm and Arrhenius that the moon and earth 
are negatively charged, and that there is a twenty-five hour period, 
but not well-defined, in the potential values, are thought to be 
largely speculative. Sohncke's experiments showing that the fric- 
tion of water vapor and ice particles can cause a marked electrifica- 
tion are treated with more consideration, though it is argued tjiat 
meteorological conditions frequently occur which would disprove 



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130 A. McADIE [vol. 11, no. 4 ] 

Sohncke's views. Exner's formula showing a definite relation 
between water vapor and electrification is noticed with the criticism 
that water vapor, so far as known, does not play the part in the dis- 
sipation of an electrical charge which the theory requires. Finally, 
the view of Arrhenius, modified by the authors themselves, is men- 
tioned. In this, the active discharging agency is the ultra-violet 
radiation. A formula may be deduced showing the relation between 
electrification and ultra-violet light. If the electrification of the air 
is positive, however, the theory falls. It is plain that there can be 
no satisfactory theory as long as the fundamental question whether 
the air contains free positive or free negative electricity or both in 
divided strata, remains in doubt. It is questionable if continued 
observations at the earth's surface will ever lead to an answer. 

Precipitation causes a disturbance of the electrical potential, and 
the constant positive values, found in clear weather, and also in the 
daily and yearly periods, disappear. Positive and negative values 
far in excess of the mean follow one another rapidly, and observa- 
tions at two neighboring stations show no agreement. With con- 
tinued rain or snow, the potential is more even. Maximum values 
occur during thunderstorms. It must be remembered that the 
flash of lightning indicates a potential difference between cloud 
and earth or cloud and cloud, exceeding a certain limiting value. 
The differences in electrometer curves during thunder, rain, hail, 
or snow storms, are differences of degree only. Our authors ad- 
vance the view tentatively, that generally the front side of a storm 
just before precipitation occurs, gives high positive values, and the 
rear of a storm high negative values, while in between occur irreg- 
ular fluctuations. The fall of fine snow is frequently accompanied 
with positive values, while large flakes give negative results. With 
lightning flashes there are rapid and marked disturbances, doubt- 
less connected with inductive effects in the collecting apparatus. 
Despite the fluctuations, there is a gradual assertion of the new con- 
dition. It will sometimes happen that the electrification of the air 
and that of the precipitation, will differ. In such a case there are 
evidently two differently charged fields. Raindrops are in general 
negatively electrified, and large snowflakes are so strongly electri- 
fied thac with a Thomson quadrant electrometer one can plainly 
note the variation when a flake falls on the collector. Systematic 
observations of the electrification of precipitation promise many dis- 
closures which will be of value in future theories as to the elec- 
tricity of clouds. As to the origin of the electricity of thunder- 



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ATMOSPHERIC ELECTRICITY 1 3 1 

storms, our authors refer to the paper by Kollert in Electrotechnische 
Zeitschrift for September, 1889. Reference is also made to Kelvin's 
recent papers on the electrification of air, where it is stated that a 
uniformly electrified globe of a metre diameter produces a differ- 
ence of potential of thirty-eight volts between its surface and cen- 
ter ; and a globe of a kilometer diameter electrified to the same elec- 
trical density would give a difference of thirty-eight million volts 
between surface and center. 

Palmieri's views on the development of electricity by the con- 
densation of water vapor remain as yet unsupported by experiment. 
The experiments of Blake and Kalischer are referred to, and while 
unquestionably good experiments, it must be noted that the condi- 
tions of the laboratory are not exactly those of nature. Faraday's 
experiments, modified by Sohncke, wherein a jet of saturated air 
under pressure plays upon a piece of ice below the freezing point, 
is next touched upon. Lenard has shown that ice will be posi- 
tively electrified by friction with water. It is necessary, however, 
to prove that ice crystals and water exist in sufficient quantity. 
The next question is that of the electrification of the air by falling 
drops. Lenard's observation is significant that the potential of the 
air is negative in the neighborhood of waterfalls, and the more 
marked the purer the water. It is said that sparks may be obtained 
by elevating rapidly a flame collector in the vicinity of a cascade. 
The seat of the free electricity is not in the drops, but in the air 
which moves. It is evident that the electricity developed in the 
neighborhood of waterfalls has not its origin in the earth's field. 
The authors mention certain cataracts which are screened from the 
earth's field, yet act like unscreened falls in producing a negative 
electrification. The electrifying of the air by the spray from ocean 
waves is touched upon, and the experiments of Kelvin and Exner 
are cited. These ways of developing electricity seem hardly ade- 
quate however. All difficulties would vanish if we could prove in 
the thunderstorm a direct transformation of the mechanical energy 
into electrical energy. 

Pellat's hypothesis of a cloud charged in the earth's field, posi- 
tively on its under surface and negatively on its upper surface, and 
the subsequent division of the cloud, overlooks the fact that the 
assumed development could only occur on a conductor, and clouds 
composed of separate drops do not permit this assumption. (This 
theory was in large part disproven, it seems to us, by Rowland and 
Morrill in a paper which is probably unknown to the authors.) 



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132 A. McADIE [Vol II, No. 4- 

Does cloud formation apart from precipitation influence the poten- 
tial ? Little can be said definitely as yet. Often the values observed 
under a sky covered with cumulus and stratus clouds do not differ 
from those of a clear sky. Ground fog at freezing temperature or 
low, generally causes a marked increase in the values. Herr 
Baschen found, while passing over a cloud in a balloon at a height 
of 3,700 metres, a distinct positive indication stronger than while in 
the free air. This observation deserves special notice. 

Concerning the relation between cosmic phenomena, such as sun 
spots or solar periods, we can yet consider only that these act indi- 
rectly. The last division of the paper deals with St. Elmo's fire 
and discharges of the brush type. Peter Lechner has for several 
years recorded these appearances on the Sonnblick. It is said that 
these displays are never noticed under a clear sky. 

With regard to ball lightning our authors do not agree with the 
views of Plants, but consider the experiments of Righi of more 
weight. Heat lightning is held to be, for temperate climates, the 
reflection of distant lightning so far away that no sound of thunder 
is audible. 

With regard to auroras, the observation of the Swedish Polar 
Expedition is noticed, where a fall in potential even to a negative 
value was observed during an aurora. The authors made some ex- 
periments on March 30, 1894, at Wolfenbiittel, during magnetic dis- 
turbances, but without success. But even had the weather been 
favorable, it is doubtful if the electrostatic and electromagnetic fields 
could have been experimentally correlated. I,emstr6m's experi- 
ments are referred to, but we think that these experiments are not 
now generally accepted. Paulsen's views and the general questions 
of the relation of auroras to magnetism are touched upon briefly. 



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ACCOUNT OF A COMPARISON OF MAGNETIC INSTRUMENTS 
AT KEW OBSERVATORY. 1 

By C. Chree, Sc. D., F. R. S., Superintendent. . 

Last July, M. T. Moureaux, of the Pare Saint-Maur Observatory, near 
Paris,, brought over to England the traveling instruments employed in 
his magnetic survey of France, and a comparison was made between 
these and the standard magnetic instruments at Kew Observatory. At 
the expressed desire of the Kew Observatory Committee, I submit on 
their behalf a brief account of the comparison and its results. 

The comparison serves to connect the standard instruments at Kew 
Observatory with the standard French instruments at Pare Saint-Maur, 
the latter, as M. Moureaux has had the goodness to inform me, being in 
excellent agreement with his traveling instruments. Pare Saint-Maur 
may be regarded as the base station for M. Moureaux's great survey of 
France and Algeria, while Kew Observatory performed a similar function 
in the surveys of Great Britain and Ireland, by Professor Riicker and Dr. 
Thorpe. The existence of the English Channel introduces uncertainty 
into any conclusions based on the trend of the magnetic lines in France 
and England, and the instruments employed in the two countries are 
sufficiently dissimilar to justify skepticism as to their close agreement in 
the absence of direct experiment. The interest of the comparison is thus 
far from being limited to the two observatories most immediately con- 
cerned. 

M. Moureaux's observations at Kew Observatory occupied the after- 
noon of July 26, and the forenoons of July 27, 28, and 29. On the after- 
noons of the last three days, observations were made with the Kew 
standard iustruments, by Mr. T. W. Baker, chief assistant at the Observ- 
atory. All the observations were made in the " magnetic house " in the 
Observatory garden. 

The comparison was really between M. Moureaux's absolute instru- 
ments and the Kew absolute instruments; but the observations, being 
made at different hours of the day, had to be connected through the in- 
termediary of the curves from the self-recording magnetic instruments. 
The elements recorded photographically are the declination, horizontal 
force, and vertical force. The value in magnetic units of 1 cm. of the 
ordinates is known, but the value of the base lines, answering to zero 
ordinates, of the several curves, is to a certain extent variable. The usual 
practice at Kew Observatory is to treat each month separately, deducing 

1 A communication to the Royal Society of London. 

.4 133 



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134 C. CHREE [vol. ii, no. 4 J 

the value of the base line for any element from a comparison of the ab- 
solute observations for that month with the curve ordinates at the times 
of the observations. 

In the case of the declination and horizontal force, the standardization 
of the curves is comparatively simple. In the case of the vertical force, 
the influence of temperature is unfortunately somewhat large, a rise of 
i° F. equaling in effect a fall of ooooi C.G.S. unit in the vertical compo- 
nent. There is also the complication that what the curve gives is the 
vertical force, while what the absolute instrument gives is the inclina- 
tion. 

Thus to compare inclinometers used at different hours, one has to fol- 
low a circuitous route by way of the horizontal and vertical components, 
allowing a correction for changes of temperature in the magnetograph 
room during the observations. 

M. Moureaux observed the inclination early, and Mr. Baker late, in 
the day, and there happened to be a slight difference in the mean tem- 
perature of the magnetograph room at the times of their observations. 

Taking into consideration the above facts, and the further fact that 
M. Moureaux's visit occurred at the end of a month, it was decided to 
standardize the curves exclusively from Mr. Baker's special observations, 
on July 27 to 29. These gave three or more complete determinations of 
each element, under conditions which might be described, on the evidence 
of the curves, as an almost perfect magnetic calm. 

Mr. Baker's absolute observations and the corresponding curve meas- 
urements were in good agreement, especially in the case of the horizontal 
force, where the individual calculated values for the base line of the 
curves showed no difference greater than 000002 C.G.S. unit. 

Owing to the less direct method of comparing the inclinometers, I 
regard the results obtained for them as somewhat less trustworthy than 
the others. 

The figures under the heading " Observatory — Moureaux " are to be 

regarded as the excess in the readings of the absolute Kew instruments 

ver those of M. Moureaux's instruments, supposing the former to have 

een read simultanously with the latter. The times specified are actually 

lose occupied by M. Moureaux's observations. 







Declination 






Date 


Time 


Kew 
Observatory 


Moureaux 


Observatory- 
Moureaux 


lly 26 
27 


3.47— 4.2 P.M. 
IO.5 — IO.I8 A.M. 


17° 5'9' 
4-8 


17° 57' 
5"o 


-fO'2 7 
0*2 


27 
28 
28 
29 


I0.22 — IO.32 u 
9.9 — 9.24 " 
9.28 — 9.4O " 

11.37— 11.49 " 


60 

2'I 

3'o 
99 


57 
i'3 
i*9 
93 


+ 0-3 
-f o*8 

4-ri 
+ 0.6 



Mean + o'g 



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COMPARISON OF MAGNETIC INSTRUMENTS 



135 



Horizontal Force ] 



Date 
July 26 
27 
28 
28 
29 
29 



Time 

4.13— 4.42 P.M. 
IO.41 — 1 1. IO A.M. 

9.48— IO.18 " 
IO.43 — i*- 11 " 
IO.24 — IO.56 " 
II. I — II.31 " 



Kew 

Observatory 

C.G.S. 

0*18354 

25 
28 
20 
20 
20 



Moureaux 
C.G.S. 

0*18356 
24 
49 
39 
43 
27 



Observatory— 
Moureaux 
(Unit being 10— * 
C.G.S. unit) 

— 2 

+ I 

— 21 

— 19 

— 23 

— 7 









Mean 


—000012 C.G.S. 
unit 






INCLINATION 






Date 


Time 


Kew 
Observatory 


Moureaux 


Observatory— 
Moureaux 


July 27 
28 
29 
29 
29 


II. 15 — II.41 A.M. 
11.21 — II.43 " 

8.55- 9I8 " 
9.21— 9.43 " 
947—IO.9 " 


67 20*2' 
203 
19-8 
20*0 
20"0 


67° 180/ 
187 
17*3 
17-6 
180 


+ i-3' 
+ r6 

+ 2-5 
+ 2-4 
+ ro 



Mean 



+ 20 / 



In judging of the results, several things merit consideration. Neither 
inclinometer read to less than i', decimals arising from arithmetical op- 
erations. The Kew unifilar magnetometer reads to 10", but with M. Mou- 
reaux's much smaller instrument readings could not be taken to less 
than 30". The great skill of the two observers is beyond question, and 
the mean of several results obtained without mental bias may possess an 
accuracy greater than that which any individual reading can lay claim to. 
Still, personally, I should be very sorry to claim accuracy of the order of 
one in the last significant figure of the mean differences. 

In the use of the results, one should remember the possibility, or 
rather probability, of the occurrence of change in magnetic instruments. 

This is a vicissitude to which traveling instruments are probably most 
exposed, but even in an observatory standard it is certainly not impos- 
sible. The constant "P," appearing in the factor 1 — Pr- 1 , which allows 
for the departure of the horizontal force magnet from the ideal infinitely 
short magnet, appears to be to some extent variable, at least in the Kew 
instrument. This particular variation does not necessarily affect the 

1 [Nov. 15, 1897. M. Moureaux requests me to explain that in the present com- 
parison of horizontal force at Kew — as well as in his recent comparisons at Pavlovsk 
(St. Petersburg) and Uccle (Brussels) — he has made use of new values for the con- 
stants of the French instruments, which it is intended to apply consistently after 
Jan. 1, 1898. 

This change, entailing a reduction of 000067 C.G.S. unit in the corrected readings 
of the French standard, was postponed until the French survey should be completed, 
though the necessity for it has been recognized for some years. Particulars will be 
found in a paper by M. Moureaux in the Annates du Bureau Central MUeorologique 
de France, Vol. 1, 1896, now in the press.] 



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136 C. CHREE IVol. 11, no. 4.J 

calculated horizontal force, because the proper value of "P" for a special 
set of observations can be calculated from the experiments themselves. 
This precaution was, in reality, actually adopted in the present case. 

Still the fact that a change does take place, which, if undetected, 
would appreciably influence the results, shows that assumptions of abso- 
lute constancy are at present acts of faith, not reason. Until there exists 
a regular system of intercomparison of the instruments at different obser- 
vatories, our information on this head is likely to be limited. 

After this remark, I think I may safely utilize the present comparison 
to extend a table, 1 in which Professor Rucker and Mr. W. Watson em- 
bodied the results of their comparison of the standard instruments at 
various English and Irish observatories, made by means of traveling 
instruments, in 1895. The differences between the declination, horizon- 
tal force, and inclination instruments are given in order, one below the 
other, the unit in the case of the horizontal force being 000001 C.G.S. unit 

The table is to be read as follows: — "Standard declinometer at Kew 
reads higher than that at Pare Saint-Maur by 0*5', but lower than that at 
Falmouth by o-8'," and so on. The last column gives the differences 
from the mean instrument, so to speak, of the five observatories. 



Kew Observatory 


Kew 


Pare 
Saint-Maur 

4- 05' 
— 12 

-f 20 


Fal- 
mouth 

— 0*8' 
—18 

— 16 


Stony- 
hurst 

+ ri' 
— 6 

+ 2-2 


Valencia 
00' 

4-29 

— 18 


Mean 

4- 0-2' 

— I 

4- 0'2 


Pare Saint-Maur 


-o-5' 

+ 12 


— 


— I'3 

— 6 


+ o*6 

+ 6 


— o'5 

+41 


— 03 

4-11 




— 20 


— 


-3* 


«+• 0*2 


-3*8 


— r8 


Falmouth 


+ o-8 
+ 18 
+ r6 


+ i'3 

+ 6 
+ 3* 


— 


+ 1*9 

+ 12 
+ 3*8 


+ 08 

+47 

— 0*2 


+ 10 
+ 17 
4- 18 


Stonyhurst 


— IT 

+ 6 

— 2*2 


— o-6 

— 6 

— 02 


— i'9 

— 12 
-3'8 





— 1*1 

4-35 

— 4-0 


— 09 

4- 5 

— 2*0 


Valencia (Cahirci- 
veen) 


O'O 
—29 

+ r8 


+ o'5 
—41 
4- 3*8 


— o-8 
—47 

+ 0-2 


+ ri 
—35 
+ 40 


— 


4- 0*2 

—30 

4- 2*0 



The apparent agreement between the standard instruments at Pare 
Saint-Maur and Stonyhurst is noteworthy. The fact that the Kew stand- 
ard instruments agree so closely with the imaginary mean instruments 
was, it may be observed, not noticed by the writer until after he had con- 
structed the table. In his opinion the phenomenon is probably purely 
fortuitous. In searching, however, for explanations of the discrepancies 
between the several instruments, or in attempting to remove them, a 
consideration of the departures from the means might be profitable. 

1 Brit. Assoc. Report for 1896, p. 97. 



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ON METHODS OF MAKING MAGNETS INDEPENDENT OF 
CHANGES OF TEMPERATURE; AND SOME EXPERIMENTS 
UPON ABNORMAL OR NEGATIVE TEMPERATURE COEFFI- 
CIENTS IN MAGNETS. 

By J. Reginald Ashworth, B. S. 

[Communicated to the Royal Society of London by Professor Arthur Schuster, 

F. R. S., and read December 9, 1897.] 

The present investigation, which has been carried out in the Physical 
Laboratory of the Owens College, Manchester, was undertaken at Pro- 
fessor Schuster's suggestion, with the object of ascertaining what kinds 
of iron and steel are least liable to a change of magnetic intensity under 
moderate fluctuations of temperature. 

Specimens of steels containing severally tungsten, manganese, cobalt, 
and nickel, also cast irons, of different blends of pig irons, and of differ- 
ent percentages of carbon, were procured from a number of different 
English and Scotch firms. The size of these specimens was in general 
about 15 cm. long and 1 or 2 thick; but as it was not uniform, the di- 
mensions and weight in grams of each are given in the accompanying 
table, columns I, II, and III. 

In column IV has been entered the dimension ratio — i. e.> the ratio of 
the length to the diameter or breadth — so that a comparison may more 
consistently be made of the magnetic behavior of any two specimens. 
For thin rods, Cancani 1 finds that increase of this ratio tends to diminish 
the temperature coefficient of a magnet. 

The course of an experiment was as follows : The rod or bar in its 
normal state, or after being hardened or annealed as occasion required, 
was magnetized between the poles of a powerful electro-magnet excited 
by a battery of twenty-six storage cells. The magnet was then fixed 
rigidly in a horizontal tube, through which a stream of cold water and 
steam could be alternately passed. The tube and its contents were placed 
at a convenient distance from a sensitive dead-beat magnetometer, and at 
right angles to the magnetic meridian. The deflections of the magnet- 
ometer needle were read by the usual mirror and scale, the distance of 
the scale from the mirror being 1 meter, and from the readings were de- 
duced directly the temperature coefficient and the total irreversible loss 
of magnetism. As the deflections were never more than a few degrees 
of arc, the angles and their tangents were virtually equivalent. The in- 
tensity of magnetization in C.G.S. units or magnetic moment per unit 

! R. Cancani, Atti della R. Ace. dei Lincei, (4), 3, pp. 501-506, 1887; Wied. Beibl. % 
vol. 11, 1887. 

137 



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I3« 



/. R. ASHWORTH 



[vol. n, no. 4] 



volume, although not necessarily required, was approximately determined 
from the formula 



I = H 



2d 



tan 



in which the earth's horizontal force, H, was considered throughout as 
constant and equal to 0*18 C.G.S. unit, and also <x, the density, was uni- 
formly taken to be 78; m signifies the mass in grams; d the distance 
from the center of the magnet to the magnetometer needle ; / the half- 
length of the magnet; and the deflection. 

The process of heating and cooling the magnet was continued until 
the intensity fluctuated between two nearly constant values correspond- 
ing to the temperatures of the cold water and steam. The coefficient a y 
given in the eighth column, was then calculated by inserting these values 

in the equation ! 

lf = Ii(i—af—i). 

The irreversible loss of original magnetic intensity which results from 
a series of heatings and coolings is tabulated under the heading P in col- 
umn VII, P being calculated from the formula 

i/=if(i-fl, 

where 1/ and I,- are the final and initial intensities. 

The limits of temperature / and f in these experiments were io° to 
20 C. and about ioo° C, giving a range of 8o° or 90 . 

The centigrade scale of temperatures and the C.G.S. system of units 
are to be understood throughout. 

In every case a record has been kept of the scale readings at the 
temperatures / and f during the progress of the operations of heating and 
cooling, and the brief example here cited may be taken as typical. 

Three per cent Tungsten Steel. 





Scale readings at 




Temperature. 








/ 


/' 


Zero o*o 



65C. 


1848 






996 




1426 




7"5 


161-3 






996 




140*2 




7*5 


1602 






99-6 




137*9 




7-5 


158*8 






996 




137-9 




7*5 


158-6 




Zero — o*i 



The table which is annexed gives a synopsis of the results obtained. 

* I have followed the customary mode of writing this formula with a negative 
sign preceding the coefficient, a; and, hence, a negative coefficient indicates an in- 
crease of magnetic intensity with increase of temperature. 



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METHODS OF MAKING MAGNETS 



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or -*.*>* V;t v1«*-* v.m^»r*r. *■* Z^stlh ;{ i^c *ame Ti;ir.*^^ -r^r^: itr-i—ri — 
a* :/%r -r/^r::- -#- :n -i** *A,:t T:n.i T!i*tn trt_ier tmitijt-f ;r i-ir^errtri — cue 
^*ra-;* r,r- »-<..» t***t**n V, *m^'0^ :v. ynr.^^ -.{ ir-^z-LziZ- i. srure — :«L 
7/;- -■ >* ' rrA . -> ir* t v-, yirzi \i 'izxt -time r>t rsr tjc-cri lie ami- 
^> *ri J . .-.-.r. .-trif ▼ "i Nv» :' vr^i * vui -.tijeri 

<tAJ*» ?",*?. ; .>. -nV- *^ v: v-/:e*f »c*kliZ7 :or tt.t/t::x Turrets X^iri':} 
ar* Hh^*«*,i1 * ■**'*- krvws r^n-da^-ietic: aces;! tie !i*±ir 5;cr ar^r rrz^Crn: 
*W.< of v?...h No* ^ art-i 7 ar» kr.w^. as KT*iec* <t> : f- jar d ecr r satttL. 
ha *.5f *.>.* oro^rrv, 'A har^en:::^ e-;es -m'zjzz. tocuci a^:«riy Tliese w~-t 
V/v. --* frorr. t>jft *a2ne rvi N*- ^ wi3 siA^rietLHi*! at tie air aisrrera- 
* #r*" No ;tw ma/fe red hot. ar/i aT^-rcd t-~ r^ci w jrils t ri tie niAT- 
n>^ f.*.d No. * a *>er::n.et: of coVcIt steel »w kir-ilj sircliei b-. 
,Ur Ka^ »i and ;% proWol** -zrJsrzt- AH of these an«i the £r=t eaasrplc 
of z,w*S. \tf*z. No o os the '.:-t. art >hef:eli steels. 

A*vr.* or. w*a then d:r*^vted chirzZy to three classes: Nickel steels. 
fa At ;ror.* and ^*^! pianoforte wires. 

N'r' iCr.r, *vr ?,?.;,% — The £rst of the^e. No. 9. is a crsciKe steel fr:ts 
Kh* ff,'->! 'or.t^ir.ir.jf 1 per cent of nickel and about cy-^5 per cent cf car- 
}*/r, The n^xt two are from Gotland. They contain 2*4 per cent cf 
n\'\cr\ and o-;<> j^er cent of carbon. Nos. 12. 15, and 14 are also firom 
.V/^Und. and r on tain 3 per cent and 27 per cent of nickel They were 
V\vA\y vjpp'i'd by Mr. Ri!e>-, of the Glasgow Iron and Steel Company. 
The behavior of the last three was remarkable, as when hardened they 
#-xhibit'd a Mnall. negative coefficient On heating and cooling they con- 
tin tjoiisly lost magnetism for the first three alternations: at the fourth 
and fifth heating and cooling there was hardly any change of intensity; 
afU-r wards a small increase of intensity with rise of temperature and 
(hi WHw with fall of temperature regularly took place. In the specimen 
containing 3 per cent of nickel these operations caused a total loss of 
no l«ss than 50 per cent of the original magnetic intensity. This same 
piece was then annealed and magnetized; the coefficient was now ftastiizv, 
the intensity rather higher, and the total loss 30 per cent On rehard- 
ening, the event* first described were reproduced, the negative coeffi- 
cient and large total loss being almost exactly as before. It is very 
likely that, by carefully adjusting the degree of hardness in this kind of 
steel, a zero coefficient could be obtained. 

The 27 ]ht cent nickel alloys, after hardening in cold water, became 
almost non-magnetic, as discovered by Dr. John Hopkinson, 1 and it was 
only in this state that they were tested. No. 13 was magnetized at the 
air temperature; No. 14 at — 16 . All the other examples of nickel 
steels had positive coefficients. 

' Hopkinson, Roy. Soc, Proc, vol. 48, p. 61. 



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METHODS OF MAKING MAGNETS 



141 



Cast Irons. — Specimens of gray cast iron, as used for general cast- 
ings, made at different times and of different blends of pig irons, be- 
haved very similarly. Magnetized as supplied they did not take a high 
intensity, lost permanently 30 to 40 per cent of their magnetism, and 
had a large temperature coefficient. When hardened, their magnetic 
properties were very different; the intensity was then comparable with 
that of tungsten steel, the total loss only about 15 per cent, and the 
temperature coefficient as low as, or lower than, the best examples of 
hardened steels. In three different kinds of carefully hardened cast-iron 
magnets it was from 000016 to 000018 per degree centigrade. The 
average value for steel magnets, of a similar size tested at the Kew Ob- 
servatory, is given by Whipple as 000029. 1 The change of intensity 
with temperature is almost strictly linear in these cast-iron magnets, and 
they are very constant when subjected to blows and shocks. 

Pianoforte Wire. — Lengths of 12 cm. each were cut from a coil of 
wire, and tested after various treatments. Magnetized in the normal 
state, this material unexpectedly gave a negative coefficient When 
heated to bright redness and chilled rapidly or slowly, the coefficient 
became positive. 

As it was thus possible to change the sign of the coefficient, an at- 
tempt was made to find the particular temper which would give a zero 
coefficient. Lengths of the wire were heated severally in oil to 200 and 
260 , and in air to a temperature producing a film of oxide, and rapidly 
chilled in water. The coefficient still remained negative, and of nearly 
the same magnitude. But when heated to dull redness and quenched, 
the coefficient was very nearly reduced to zero. Heated to higher tem- 
peratures and quenched, the coefficient became positive. 



Table II 



No. 


Condition 


R = 2l/d 


I< 


1/ 


P 


OCO'OO 


1 6a 


As supplied 


109 


649*0 


644 6 


0008 


— 0023 




Tempered at 260 


44 


792-1 


769-2 


-029 — -018 




Ditto dull red 


(4 


883-0 


863 *6 


0022 


— 0002 




Ditto, ditto 


41 


892 *o 


869*0 


0*026 


+0003 
+0008 




Glass hard 


44 


559*5 


537'i 


0040 




Annealed 


44 


849*0 


830-1 


023 ' -f-o 006 


16b 


As supplied 


IOO 


679-0 


633*6 


067 —0 -055 




Glass hard 


44 


593 -o 


497 


0163 


— 0*017 



Length of each piece, 12 cm.; weight, about 09 gram; diameter, 16a = 
oil cm., i6£ = o*i2 cm. These two specimens are made from different kinds 
of steel. 

1 Whipple, Roy. Soc. Proc, vol. 26, p. 218. 
5 



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142 /• ^. ASHWORTH [Vol. II, No. 4] 

It is a curious coincidence that the intensity of magnetization at- 
tains a maximum for the condition producing minimum temperature co- 
efficient, and this maximum has the exceptionally high value of 892 
C.G.S. units. 

The fact that the negative coefficient could not be reproduced if once 
the wire had been heated above a red heat, indicates that there is some 
structure physically imposed upon music wire, perhaps in the process of 
drawing, which partly or wholly contributes in producing the negative 
coefficient. Whereas the negative coefficient in the nickel steel is repro- 
ducible, and is doubtless a consequence of intense hardness. In contrast 
with this it may be mentioned that music wires are not at all hard, being 
easily touched with a file. 

In order to gain further insight into the cause of the negative coeffi- 
cient in these wires, some experiments were made to test the effect of 
removing successively the outer layers of the wires by dissolving them 
in nitric acid. This revealed the important relation that the coefficient 
became more negative as the diameter became less, the length remain- 
ing the same — that is to say, as the dimension ratio increased. 



Curve (2) on this diagram traces the series of experiments on No. 
33 wire. The two first points on the left correspond to the coefficients for 
three and two pieces bound together, the third point that for a single 
piece, and succeeding points the coefficients for the same piece at three 
stages of dissolution. The third curve is constructed from the data in 
Table V, and represents the passage from a positive to a negative co- 
efficient in No 34 wire. 



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•[ To be inserted opposite p. 142, Vol. //.] 



ERRATA. 



1. After line 18, p. 142, proceed to line 11, p [46. and continue to the 
end of p. 149; then return to line 1, p. 143, and conclude at line 10, p. 146. 
The last seven lines p. 142 should be omitted. 

2. Omit the decimal point and prefixed cipher before the numbers 
representing the temperature co-efficient « in Tables II, IV and V. 



If curves for a and p be plotted with demagnetizing factors, i. e., the 
demagnetizing force per unit intensity, corresponding to their dimen- 
sion ratios as abscissae, they resemble, strikingly, curves of magneti- 
zation, having a point of inflection near the beginning and ultimately 
approaching horizontal asymptotes (Diagram III); by prolonging the 
curves in this diagram until they cut the axis of ordinates, it is easy to 
estimate what may be called the ♦•characteristic" temperature coefficient 
and permanent loss for this kind of wire. 



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144 /• R - ASHWORTH [voi~ 11. No. 4 ] 

It may be inferred that in general the temperature effects upon mag- 
nets are principally influenced by the demagnetizing factor over a con- 
siderable range of dimension ratios, and beyond that range by the na- 
ture of the material. 



In the fourth diagram the curves of initial and final intensities are 
plotted with dimension ratios as abscissae, and they resemble so closely 
the curve traced in the same way by Barus 1 for steel of " blue annealed " 
temper, that it is very probable this is the temper given to the music 
wires upon which these experiments have been made. 

i Barus and Strouhal, Bulletin U.S. Geol % Survey, No. 14, 1885; Terrestrial 
Magnetism, March, 1897. 



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METHODS OF MAKING MAGNETS 



145 



The chief points elicited by this investigation may now be sum- 
marized : — 

1. The temperature coefficient is generally least in the hardest irons 
and steels, and is particularly small in hardened cast iron. Certain hard- 
ened nickel steels have very small negative coefficients. 

2. The discovery of negative coefficients in music wires. 

3. Change of the sign of the coefficient by alteration of (a) temper and 
(6) dimension ratio, and hence methods of obtaining zero coefficients. 

4. Some relations between the dimension ratio and self-demagnetiz- 
ing factor, temperature coefficient, and permanent loss of magnetism 
after alternate heatings and coolings. 



An important consideration in any practical application to magnetic 
instruments of magnets with zero coefficients is the constancy of the 
zero state. 

It is not yet possible to speak precisely on this point, but two wires 
which had been prepared by adjustment of temper to have zero coeffi- 
cients in June, 1896, and since then had been lying on a shelf, and in 



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146 



/. R. ASHWORTH 



[Vol. II, No. 4-1 



the vicinity of other magnets, when tested nine months later, had not 
altered so much as to have a coefficient of practical consequence. The 
intensity had diminished, however, by nearly 25 per cent. 

Similarly the magnet which had been given a negligible coefficient 
by cutting the length of the wire to 8 cm., as cited above, after be- 
ing boiled at intervals for four hours, was found five months later to 
have changed so little that its coefficient might still be considered neg- 
ligible. 

Further experiments, however, upon this question and some others 
arising out of this investigation are now in progress. 

To verify this carefully a series of stout music wires of different 
thicknesses, but in other respects as uniform as possible, were procured 
from a manufacturer at Warrington, to whom I am also indebted for 
kindly supplying other samples of steel wire. The results of these ex- 
periments are most conveniently exhibited in tabular form, and are here 
annexed. 

Tabjcb III 



No. 


d 


tn 


R 


I. 


1/ 


P 


a 
000 


a xd 

O'OOOO 


33 


0216 


3 535 


55*3 


530*3 


428-5 


0*192 


—0136 


294 


30 


0187 


2 59° 


63 *8 


592-8 


508 6 


0*142 


—0184 


344 


28 


0174 


2*235 


69 


632*4 


551*5 


0128 


— 0226 


393 


26 


oi53 


1 760 


78 


736-0 


652*8 


0*113 


—0203 


3io 


24 


o'i34 


1*365 


890 


742-o 


686-3 


0*075 


—0306 


410 



Length of each piece -— 12 cm. 

With the exception of No. 26 (and No. 26 was anomalous in some 
other respects) the coefficients become progressively more negative as 
the dimension ratio increases. The increasing product of the coefficient 
into the diameter shows that the coefficient changes more rapidly than 
the dimension ratio. The table also shows the regular diminution of the 
permanent loss, ,.*, and increase of intensity as the dimension ratio in- 
creases, relations which hold in further experiments of the same kind 
to be described later on. 

Several of these wires, after being thus tested, were dissolved in nitric 
acid, and the temperature coefficient determined at successive stages of 
: process without any remagnetization of the wire. The results of 
. 33 alone are here giveu, as they sufficiently exemplify what gener- 
Y takes place under these circumstances. The negative character of 
: coefficient progressively increases with increase of dimension ratio, 
i at a rather greater rate as in Table III. 



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METHODS OF MAKING MAGNETS 
Tabi^e IV 



147 



No. 


d 


nt 


R 


li 


V 


p 


a 1 ax d 
O'OO 1 -oooo 


<u 33 
> ( 1st stage 
S -j 2d stage 
£ I 3d stage 


0*216 

OI95 1 
0-163* 

Q-II2 1 


3*535 
2*875 
1*995 
o*935 


55*3 

61 *3 

73*6 

107*5 


530*3 
478*0 

474*5 
485*5 


428-5 

464-6 

4689 
482-9 


-192 
0*028 

0*OI2 
OOO5 


— -0136 294 
— 0155 302 
— 01961 319 
— -0292! 327 



It is interesting to observe in these experiments the increase of in- 
tensity each time the wire is redissolved, remembering that after the initial 
magnetization the wire was not subjected to any further magnetizing pro- 
cess. Thus, for example, No. 33 has an intensity, after being heated and 
cooled, of 428; upon dissolving off an outer layer the intensity rises to 
478, which in its turn is reduced by heatings and coolings to 465 ; dis- 
solving it a second time raises the intensity to 475, and so on. The re- 
covery of magnetic intensity after dissolving in acid is most likely to be 
ascribed to diminution of the self-demagnetizing force resulting from 
increase of dimension ratio. The intensities, however, after each dis- 
solving, namely 478, 475, 486, are sufficiently constant to indicate that 
the intensity is nearly uniform throughout the wire, and this confirms an 
experiment of Bouty's. 2 

The next two wires have been grouped in a separate table from the 
others, as they came from a different factory, being made in Sheffield. 
They are thicker than the former wires, and the thicker of the two, No. 
34, has now a positive coefficient. By continually reducing the diameter 
of this wire, the coefficient ultimately changes sign and becomes neg- 
ative. 

Table V 





No. 


d 


m 


R 


I, 


1/ 


P a 














j o-oo 


32 


0227 


3*875 


52*8 


490*1 


340-6 


0-305 1—0-0015 


•2 ** 


0262 


5*145 


45*8 


388-6 


271 9 


0*304 40*0220 


> 


' 1st stage 


O 2 23* 


3*740 


53*7 


307*2 


299*2 


0-026 -f 0*0193 





2d stage 


-204 1 


3*130 


58 7 


297*9 


290*3 


0*025 1 -+-0*0184 


0) " 
0) 


3d stage 


0-I52* 


1742 


78*8 


306-6 


300-2 


0*021 |-j-0'0082 


Q 


L 4th stage 


O 075 s 


0427 


159*2 


292*5 


287-1 


0*019 I — O'OIOO 



Length, 12 cm. 

And it may be calculated that if No. 34 had just been dissolved so 
far as to have a dimension ratio of about no to 115, it would have ex- 

1 Calculated from the weight. 

*Ann. Scient. deVEc. Norm., [2], 5, p. 131. 

•Calculated from the weight. 



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148 



J. R. ASHWORTH 



[Vol. II, No. 4-] 



hibited a zero coefficient. Since the former series of wires with dimen- 
sion ratios of this magnitude would have had large negative coefficients 
there must be some important physical or chemical differences between 
these and the former wires influencing the character of the coefficient. 

To complete the series of experiments on the influence of the dimen- 
sion ratio it was desirable to perform the converse operation and to 
prove that an originally negative coefficient would become positive by 
increase of thickness. 

Three pieces, (0), (£), (c), of No. 33 wire were cut from the same coil, 
each 12 cm. long, magnetized and then heated and cooled separately in 
the same way. The coefficient was about — 0-000119 for each, (a) and 
(b) were then bound together with fine copper wire like poles being in 
contiguity; the coefficient as now determined was almost zero. The 
piece {c ) was then joined in the same manner to its two fellows and the 
coefficient again determined; it was now +0*000105. The experiment 
is conclusive, for it is allowable to regard bundles of wires as rods of 
equivalent cross section. 1 

Wires drawn to different thicknesses are not structurally sufficiently 
identical to allow of strictly comparable magnetic results. It is therefore 
more satisfactory to vary the dimension ratio by altering the length and 
keeping the diameter constant. A series of tests were conducted in this 
way. Lengths of 3, 6, 9, 12, 15, and 18 cm. of No. 30 wire were cut 
from the same coil, separately magnetized, and the coefficient of each 
very carefully determined. Table VI gives a complete view of the re- 
sults. 

Table VI 



No. 


2/ 


R 


Ii 


/ 


P 


a 
o*oo 


30 


3 cm. 


15*95 


137*4 


787 


0427 


-f-0261 


i< 


6 " 


31*90 


313*4 


204*0 


o*349 


+0151 


i< 


9 " 


47*85 


483*2 


378*3 


0*217 


— 0084 


« 


12 " 


63*80 


602 *o 


513*8 


0147 


—0225 


it 


15 " 


79*75 


683 1 


595 


0*129 


—0296 


<< 


18 " 


95 7o 


726*8 


637*4 


0123 


—0317 



Diameter of each piece, 0*187 cm - 

The cofficient changes from positive to negative between the lengths 
6 and 9 cm. And hence if the change between these points is nearly 
linear, a length of about 8 cm. should have a zero coefficient, and it 
might also be calculated that the permanent loss would be 0262. A 
fresh length of exactly 8 cm. was cut from the same coil of wire and 
was found to have a coefficient of — 0000015, an< * a permanent loss of 

1 Van Waltenhofen, Wien. Ber., vol. 48, part 2, p, 578, 1863. Ascoli and Lori, R. 
Acad, dei Lincei, Rome (5), 3, 2 Sem., p. 157, 1894. 



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METHODS OF MAKING MAGNETS 149 

0-281. A piece of this wire, a very little less than 8 cm. long, would, 
without doubt, have a strictly zero coefficient. 

There are thus two practicable ways of obtaining zero temperature 
coefficients, either (1) by altering the hardness, or (2) by altering the di- 
mension ratio; and the latter may be effected by varying the diam- 
eter for a constant length, or the length for a constant diameter, 
as may be the more convenient. In addition, the material of which 
the magnet is made must have certain chemical and physical properties, 
not yet determined, of which as far as some experiments I have made can 
decide, the physical rather than the chemical properties are the more 
important. 

Some of the results in Tables IV, V, and VI are here plotted as 
curves and exhibit interesting features. 

The curve of the relation of coefficient to dimension ratio (diameter 
constant) from the data of Table VI, Diagram I, curve (1), has a double 
inflection between which it crosses the axis of abscissae and at either end 
apparently approaches to horizontal asymptotes. This curve is prob- 
ably typical of the behavior of music wires. 

Curve (2) on this diagram traces the series of experiments on No. 33 
wire. The two first points on the left correspond to the coefficients for 
three and two pieces bound together, the third point that for a single 
piece, and succeeding points the coefficients for the same piece at three 
stages of dissolution. The third curve is constructed from the data in 
Table V, and represents the passage from a positivo to a negative co- 
efficient in No. 34 wire. 
6 



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THE MAGNETIC CONDITION OF THE EARTH EXPRESSED AS A 

FUNCTION OF THE TIME BY V. CARLHEIM- 

GYLLENSKOLD.i 

Reviewed by Dr. Adolf Schmidt (Gotha). 

It is doubtless generally recognized that all attempts hitherto made 
to express the secular variation of the magnetic elements by means of 
formulae were in the nature of preparatory or preliminary investigations. 
The derived formulae, invariably referring to particular stations, were 
purely interpolation formulae, the apparently simple law revealed in gen- 
eral by the formulae being the only fact of material significance. L. A. 
Bauer's well-known thesis, however, in which for the first time a law 
governing the secular variation over the greater portion of the earth was 
shown to hold true, marked an important step forward. 

The natural method to be pursued in a theoretical investigation of the 
secular variation was clearly indicated in Gauss's analytical representa- 
tion of the earth's magnetic potential. In this representation, the mag- 
netic condition of the earth was expressed as a function of the geograph- 
ical coordinates without making any assumptions whatsoever with 
regard to the distribution of the earth's magnetism (with the exception 
of the one, fully justified by the results obtained, that the earth's entire 
magnetic force could be referred to a potential of internal forces alone). 
This analytical representation then formed the simplest and surest basis 
for all further theoretical investigations. One step, however, remained — 
to express likewise the magnetic condition of the earth as a function of 
the time. The magnetic condition at any time being expressed in the 
only form suitable, that of solid spherical harmonic functions, the intro- 
duction of the time variable could only be accomplished with the aid of 
a similar series of terms, in which, however, the coefficients would be 
functions of the time. 

The author of the paper before us deserves the credit of being the 
first to undertake and complete a solution of this problem. From the 
results obtained he has also drawn important conclusions respecting the 
possible physical cause of the secular variation. On account of its val- 
uable contents, and by reason of the manner in which the investigation 
was carried out, this paper must henceforth be classed among the funda- 

i Carlheim-Gyllenskold, V : Sur la forme analytique de ^attraction mag- 
nStique de la terre exprimee en fonction du temps. Astronotniska Jakttagelser och 
Undersokningar anstalda pa Stockholms Observatorium. Bd. V, Heft 5. Stock- 
holm, 1896. 20x25 cm. Pp. 36. Three inserts. [The review is translated from 
the Meteor ologische Zeitschrift for June, 1897.] 

150 



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THE MAGNETIC CONDITION OF THE EARTH 151 

mental works of terrestrial magnetism. One fact should also be men- 
tioned, viz., that this small, compact pamphlet is the product of an 
immense amount of computing ; for those not acquainted with such com- 
putations can scarcely appreciate the magnitude of the work involved. 
The author's industry is all the more astonishing, as he has published 
within the last few years a whole series of time-consuming researches. 

The basis of the entire investigation consists of the computation of 
the earth's magnetic potential for various epochs. (The introduction of 
the hypothesis of a potential and only of internal forces is of course here 
entirely permissible. It may be well to state, however, that even in case 
future researches should conclusively prove that these hypotheses are 
not quite correct, we still can, and, in fact, must make use of them in 
investigations referring to early periods. From the results of the review- 
er's potential computation, and from those of the related investigations 
of Schuster, Rticker, and the author, it follows that the state of our 
knowledge of the distribution of the magnetic elements is not sufficient 
to permit our making a safe decision as to the admissibility of the hy- 
pothesis of a potential, and that with the aid of this assumption a repre- 
sentation sufficiently accurate for the present, is obtained. And this is 
all the more true for the old observational data. In this way the present 
problem is decidedly simplified.) 

An insurmountable difficulty for this investigation, however, is the 
fact that we possess no intensity observations for the early periods. For 
the determination of the potential the most complete knowledge of the 
direction of the magnetic force, viz., of declination (6) and inclination (* ), 
does not suffice; we must know in addition the intensity at one point at 
least in every equipotential line, or, say, along a curve intersecting all 
equipotential lines. Without the aid then of arbitrary or hypothetical 
auxiliary conditions we can not accomplish more than the determination 
of a function, whose lines of equal values would coincide with those of 
the potential function, the relation between the two functional values 
from line to line, however, not being the same. The function derived, 
therefore, in whatsoever manner from values of declination and inclina- 
tion alone, can not be strictly designated as potential, even though, as 
may easily be possible, the two functions differ very little from each 
other. For the comparison of the computed directions of the magnetic 
force with the observed ones, this fact is, however, of no importance. 
Still, it seemed desirable to the reviewer to call attention to a matter 
that apparently has not as yet been sufficiently emphasized, especially 
as the author's theoretical developments might easily give the impression 
that by his method of successive approximations it would be possible to 
compute intensities with a decree of accuracy alone dependent upon the 
precision of observational data (<5 and *). 

The problem to compute the potential (in the sense expressed above) 
from observations of declination and inclination has already been inves- 



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l 5 2 V. CARLHEIM-GYLLENSKOLD [vol. ii, no. 4 .) 

tigated by L. A. Bauer. 1 His method, which consists in the elimination 
of the intensity from the equations for X and K, is theoretically the 
simplest and best. Practically, however, there is the disadvantage that 
it does not permit the division of the unknowns into several groups to be 
separately determined, and that in repeating the computation for different 
periods or for different material, no marked simplification is possible, so* 
that the application of the method would involve an extraordinary 
amount of labor. In even greater degree does this disadvantage make 
itself felt, if we undertake, as the author of the paper before us at first 
attempted, to represent the secular changes of the declination and incli- 
nation (d& and di) % during a certain time interval, by the variations of 
the coefficients of the potential expression, and then to compute the 
coefficients — a problem of which the author has given two theoretical 
solutions. For the practical accomplishment of his object, therefore, he 
makes no use of these solutions, but uses instead an approximation 
method. 

Suppose for any period / the potential V\ be represented by an ex- 
pression of the form 2 »c „,< P n or briefly 2c* P in which Ct stands for the 
desired coefficients (the g's and h's according to the Gaussian notation), 
and P for the known spherical harmonic functions for every station. 
For the components of the force we have then : 

X =1 c. /*, Y--- 1 c. P\ Z=2 c, /*", 

in which P\ P'\ P"' are also known quantities related with P. 
Let V now be the known potential for some recent period /„, and 
V\ the potential for a somewhat earlier period A . We know, in other 
words, the values of Co and wish to find those of c\ . Our data are either 
the declination changes (d <*), or those of the inclination {d *), or both for 
the time interval between ti and /» at a sufficient number of well dis- 
tributed points. If //now is the horizontal in ten si ty,* we have: 



d Y=H cost.d d+ sin d . d H 
d Z=H sec* i . di+ tang i .d H 



-.}■ 



The author for the purpose of a solution at first puts d //=o, so that 
we have : 

I dcx . P" = H cos * . d d , l 
Idcx .P"'= //sec' i.di . \ 

Substituting the values of P" and P"\ those of 6 or i (the mean val- 
ues for t\ and t ), and of H for t Q , the author obtains for every station 

x Proc. Am. Assoc, for the Adv. of Sc. t Vol. XLIII, 1894. Review in Fort- 
schritte der Physik, LI, 3, Abth. p. 552. 

[*The author and the reviewer use R to represent the horizontal intensity, and 
then again to represent the earth's radius. The liberty has been taken to substitute 
H for R in this place.— Ed.] 



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THE MAGNETIC CONDITION OF THE EARTH 



153 



an equation — two, if both <* and i are used — involving the unknowns dc\ . 
These can then be computed, and hence the values of c\ == c n — dc\ can be 
obtained, thus giving a first approximation to V\ . From V\ in turn H 
for the epoch /1 is derived, and hence the approximate value of dH for 
each station, making it possible then to recompute V\ , using now the 
figorous equations (a). This method, if need be, can be repeated several 
times. In a similar manner we can retrogress from V\ to V% , and 
thence to Vs , etc. 

Starting with the Erman-Petersen potential expression for 1829, the 
author has derived Ffor the epochs J 787, 1700, and 1600, using both 
declination and inclination data for the first two epochs and declination 
data alone for the last one. In the first approximation, the spherical 
harmonic series was limited to the eight terms of the first and second 
order. To these results he adds those for 1784 and 1858 (based upon 
Erman-Petersen's work), for 1830 (according to Gauss), for 1880 (from 
Quintus Icilius), and for 1885 (from Neumayer-Petersen), and seeks now 
the law of the dependence of the several coefficients upon the time varia- 
ble. He finds such a law, in fact, and this constitutes the chief result of 
his work. It is the simplest law to be expected a priori, and is fully 
verified, as we may state in advance, by the results of the second approx- 
imation. 

If we write the potential V (or rather the quotient V : R, in which 
R is the earth's radius) in the form : 

oj /» + aj PI + . . . . 

+ «! COS (X + |5|) P\ + a? COS (* + #)/?+.... 

'+ aj COS 2 (JL + $[)/>?+ . . . . 

+ . . . . 

So that comparing with Gauss's notation we have generally : 
<C cos m (I + ft) = g n M cos ml 4- hi sin ml 

It is found that, within the limits determined by the observation 
errors, the coefficients «* may be regarded as constant, and the angles ft as 
varying uniformly with the time. 

This law otherwise expressed is : The separate parts of the potential 
(which are multiples of the individual P^) revolve about the earth's rota- 
tion axis, each with a different velocity, but none suffering any change 
in magnitude. (Since this law does not hold for a transformation of co- 
ordinates it follows that within the limits of its validity the cause of the 
earth's magnetism stands, with a degree of probability bordering on cer- 
tainty, in some relation to the position of the earth's axis, and hence to 
the earth's rotation — a conjecture which has been made, in fact, repeat- 
edly, and proof of which has been often attempted from various stand- 
doints.) 



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i 5 4 V- CARLHEIM-GYLLENSKOLD [vol. ii, no. 4 ) 

Having thus obtained the means of computing approximate values 
for <* and i for any epoch, the author next carries out a second computa- 
tion, this time to terms of the fourth order (24 coefficients), using the 
same method as before, except that the differences dc now denote the 
corrections to be applied to the approximate values already obtained. 

With the aid of a number of old observations found by him, the author 
constructs isogonic charts for the epochs 1538, 1572, 1600, 1642, 1676, and 
1 700, of which the first four do not, of course, embrace the whole earth. 
It is hoped that these observations and their critical discussion may at 
some time be published. The computation spoken of is now carried out, 
as based on these charts, on those of Hansteen for 17 10, 1720, 1730, 1744, 
1 7S^ l 77°> 1780, 1787, and 1800, and upon those constructed with the aid 
of the more complete material (<*, /', //) for 1820, 1840, and i860. Em- 
ploying the results of the well-known potential computations for 1829, 
1830, 1880, and 1885, he obtains finally, for 22 time periods, the coeffi- 
cients g^ and h n m of the potential, and hence the values of <£ and /T, which 
confirm the statement already made, that it is at present sufficiently pre- 
cise (especially for the terms most accurately determined — those of the 
1 st and 2d order) to put 

< = const, and Al = r*» + »C t 

He then determines the final values of the a n m with the sole aid of the 
modern observations embracing intensity determinations. The argu- 
ments /'£, however, are derived with the aid of all the results, giving less 
weight to the early ones. The following table gives these values, / be- 
ing counted from 1800: 

«1 = +0.322946 

a\ = +0.067055 y\ = 59°.307 ml = +o°.ii438 

«J = +0.001506 

a[ = +0.047815 f x = i68°-333 m? = +o°. 26062 

«5 = +0.013244 r* = 27°.646 mj = +o°.39585 

«J = — 0.017527 

a J .— +0.039018 y\ = 329°-34i m? = + o°.27i97 

aj= +0.028373 yi= 85°.688 m? = +o°.oo540 

a\ = +0.007474 rJ = 25°.503 m5 = +o°. 14729 

«J = — 0.026447 

a{ = +0.040680 r\ = i87°.775 mf = —o°. 14039 

a* = +0.022249 r\ = iii°.964 mj = — o°.n872 

a* = +0.008200 /* = 345°.846 mj = +o°.o89i9 

«1 = +0.001 155 y\ = 65°.289 mj = +o .O592o 

From the values of «J, «}, and m\ % it results that the earth's magnetic 
moment is constant (viz., 853X io' 25 cm 6 /* g H , s~ l ) and that the magnetic 
axis forms a constant angle of n° 44 / with the rotation axis, revolving 



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THE MAGNETIC CONDITION OF THE EARTH 155 

uniformly about the latter axis once in 3,147 years in an east-west direction. 
The other terms of the potential series pass through their variations in 
shorter periods, this fact having a special significance for the observa- 
tion series of stations which apparently disclose a secular period of but 
a few hundred years. Thus, in the series for X, Y, and Z, the period of 
the term with P\ is 454 years, and that with P\, 815 years. 

As an illustration of the application of his formula, the author com- 
putes the declination, inclination, and total intensity for 134 uniformly dis- 
tributed stations, differing from each other in latitude 15 and in longi- 
tude 30 . The computed values of the declination are compared with 
those obtained from the observations. The residuals are at times some- 
what heavy, yet a graphical representation presents on the whole a sat- 
is factory agreement. To test the computed inclinations, a comparison 
is made with collected inclinations observed at the end of the sixteenth 
century and beginning of the seventeenth. 

In the last paragraphs an attempt is made to find a physical ex- 
planation of the results obtained. We can speak but briefly of this part 
of the investigation, and we must likewise content ourselves with a bdre 
reference to Schuster's closely related investigation contained in Ter- 
restrial Magnetism, Vol. I, p. 1. It is found that the variations of the 
earth's magnetic condition can be referred to the inductive action of an 
external magnetic field, whose separate parts, expressed in spherical 
harmonics, are small fractions of the corresponding harmonic terms of 
the earth's magnetic field, and are displaced, with reference to the latter, 
by the angle * : 271 towards the west. It is further found that such an 
external field is brought forth by the earth's inductive action in case 
the upper layers of the atmosphere are conducting and lag behind the 
earth's rotation so as to have a relative motion from east to west. (The 
reviewer's computations respecting the earth's magnetic condition for 
the year 1885 disclosed such an external field, the principal part of 
which, however, was displaced with reference to the internal field to- 
wards the east instead of to the west. It is quite possible, however, that 
this departure of his results from those required by the outlined theory 
may be due to inaccuracy of the data of observation, and hence his re- 
sults must not therefore be regarded, at present, as deciding conclusively 
against the theory.) Qualitatively the author's explanation of the sec- 
ular variation suffices. There remains to show that it will also satisfy 
the observed facts quantitatively without the necessity of making im- 
probable assumptions as to the conductivity of the upper atmospheric 
regions and of the inductivity of the earth. 

In conclusion, the author refers to the necessary modifications that 
must be made to the theoretical results as obtained on the assumption of 
the homogeneity of concentric layers of the earth to meet the case in 
nature — which modifications one must expect will reveal themselves by 
a closer investigation of actual phenomena. 



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LETTERS TO EDITOR 



THE ASSAM EARTHQUAKE OF JUNE 12, 1897— A REQUEST 

FOR DATA. 

The Editor takes great pleasure in inserting the following extract 
from a letter recently received from Professor William Morris Davis, of 
Harvard University. It is hoped that those having the required data 
will communicate with Mr. Oldham. 

"Mr. R. D. Oldham, of the Geological Survey of India, Calcutta, de- 
sires to secure records from seismographs and magnetic instruments that 
may show indications of disturbance on June 12, 1897, the date of the 
great earthquake in Assam. Mr. Oldham has already issued a report on 
the earthquake, and wishes to carry his investigations further, after 
gathering fuller data." 



THE LATITUDE VARIATION AND THE EARTH'S MAGNETISM. 

Some two months ago, while speculating about the possible indirect 
effects of the lately discovered variation of latitudes, the idea occurred 
to me that possibly the magnetization of the earth is subject to a varia- 
tion with a period of 428 days — the latitude period. 

The earth is a great magnet. If a magnet is subjected to stress, its 
magnetic state is slightly changed. Why should not the great stresses 
produced in the earth by the shifting of the pole of rotation produce a 
change in its magnetic state ? Is it not possible also that one effect of 
these stresses may be to produce local periodic earth currents which mod- 
ify the magnetic elements at each station? 

Such was the speculation which led me to examine such long records 
of magnetic observations as were immediately accessible to me ; namely, 
those published in various reports of the United States Coast and Geod- 
etic Survey. The examinations thus far made, by the use of the har- 
monic analysis, have produced a strong conviction, — though not a feel- 
ing of certainty, — that the magnetic elements at any station are subject 
to a variation with period of 428 days. I have not as yet had time to 
revise my computations carefully, and so do not care to announce nu- 
merical results at present. In another month I hope to be able to furnish 
the Journal the revised results of my present computations, and to ex- 
tend the investigation to other long series of magnetic observations. 

John F. Hayford. 

Cornell University, Ithaca, N. Y., December 24, 1897. 
156 



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NOTES 



OBITUARY. 
It 19 with great regret that we record the death, on November 2, 1897, of 
the Director of the Gauss Magnetic Observatory, Ernst Schering, Professor 
of Mathematics at the University of Gottingen. A notice of Professor 
Schering's papers on terrestrial magnetism will appear later. 



THE MAGNETIC "VARIATION" AND DIP FOR THg YEAR 1897. 

The Journal has received from Mr. G. W. Littlehales a copy of his re- 
cent chart giving the isogonic and isoclinic lines over the entire earth for 
the year 1897. This finely executed magnetic chart, 113 X 58 cm. in size, is 
published by the United States Hydrographic Office and sold for fifty cents. 
For the purpose of reducing old data to date of chart, Mr. Littlehales 
makes use of the many secular variation formulae deduced by him, notices of 
which have already appeared in the Journai,. We trust that he will be able 
at no distant day, to publish likewise the data upon which his chart is based. 



THE MEAN VALUES OF THE MAGNETIC DECLINATION FOR 
PARALLELS OF LATITUDE. 

Dr. van Bemmelen in a recent paper ' has inadvertently misquoted a con- 
clusion reached by me some time ago with regard to this subject. He says : 
"Dr. Bauer {Am, Jour, of Science^ Vol. I, 1895, p. in) has computed the 
values of the mean declination for the period 1 780-1885, and finds that they 
are invariably positive. Again he finds that the values vary with latitude, but 
that the variation is too small to permit the drawing of any definite conclusion. 
I, however, find just the reverse : positive and negative values of the mean 
declination and a typical change with latitude; viz., a decrease [beginning 
with 70 N.] until a low northerly latitude is reached; then an increase up to 
high southerly latitudes, followed by a decrease again." 

As a matter of fact, Dr. van Bemmelen's conclusions are a confirmation 
of my own, not a contradiction, as will be seen below. On p. 113, I give the 
following conclusion among others: "The mean declination along a parallel 
of latitude is always westerly [positive], the minimum occurring near the 
equator; the quantities, in general, increase upon leaving the equator." 

Below will be found a tabular presentation of our respective values of the 
mean declination. Table II is taken directly from my publication cited by 
Dr. van Bemmelen, and it will be noticed that for every one of the years given 
the figures reveal the characteristic change with latitude. 

1 Werte der erdmagnetischen Declination fur die Periode 1500-1700, etc. [Cf. p. 162.1 
7 157 



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I5« 



NOTES 



[VOL. II, NO. 4] 



Tabi,e I 
Van Bemmelen's values of the mean magnetic declination for parallels 

of latitude. 



Year 




















Equa- 











1 




Antarctic 




70 N '60 50 


40 


30 I20 

1 


10 


tor 


10 .20 

1 


30 


40 


50 |6o 


Circle 






















1 













1600 8.0WI3.4W 


1.1 W 


0.1 E 1.1 EI1.4E 


1.2 E 


0.3 E 


0.4WI0.3W 


0.2 E 


0.7 E 


1.5EI2.0E 




1650 8.5 4.1 


2.1 


0.5 Wo. 1 W^o.o 


0.1 W 


0.4 W 


0.8 |i.o 


1.0W 


1.2 W 


0.7W11.3E 




1700 


9.4 W 5.1 


2.9 


0.7 0.2 10.4W 


0.6 


0.6 


O.7 jl.2 


J -3 


1.3 


0.8 0.6 E 




1770 




2.4 


1.2 


0.4 I0.4 0.3 


0.3 


c.5 


0.8 1 1.O 


1.5 


2.3 


2.5 I3.4 w 


31 w 


1842K 




2.8 


1-7 


1.2 ,0.5 '0.5 


o.5 


0.8 


1.2 1 1.5 


2.0 


2-3 


2.4 ,2.4 


1.4 


1885 


3.0W 1.4 w 


0.6 WI0.4 W0.5 w 0.6 w;o.9 w 


I.2W|l.8W 


2.6 W 


3.5 w 


4.0 W 4.0 W 


35 w 



Table II 

Bauer's values of the mean magnetic declination for 
parallels of latitude. 



_ — _. j — 


Year 



60N 


1 

1 

40 120 

1 


Equa- 
tor 



20 



40 


6o°S ' Mean 




. 











1 


1780 


2.2 W 


1.1 W 0.5 W 0.5 w 


1.1W 


2.3 w 


2.8W1.5W 


1830 


2.0 


0.7 


o-3 


o-5 


1.3 


2.7 


1.4 1.3 


1842 


30 


1.0 


0.2 


0.2 


1.4 


3.0 


2.1 


1.6 


1858 


3-7 


1.0 


o.3 


0.7 


1.6 


3-2 


2.4 


1.8 . 


1872 


3-i 


0.7 


0.2 


0.8 


2.0 


3-3 


3-2 


1-9 


1880 


2.0 


0.8 


0.4 


0.9 


1.8 


34 


3-5 


1.8 


1885 


2.5 w 


0.7 W 


04W 


1.0W 


1.8 W 


35 w 


4.iWj2.oW 


Mean 


2.6 w 


0.9WI0.3W 


0.7 W 


1.6W 


32 W 


2.8WI1.7W 



With regard to the signs of the mean values, i. e. whether westerly or 
easterly, it will be noticed that all the values in Table II are westerly, and 
that in Table I some easterly values occur for the years 1600, 1650, and 1700. 
It is not possible at present to say how much reliance is to be put upon the 
early values, especially as they are of but small magnitude. For example, I 
obtained some easterly values from van Bemmelen's first magnetic charts for 
latitudes, which now give westerly values, as resulting from his later work. 

A word might be said with regard to the value of such investigations. 
Of course, neither Dr. van Bemmelen nor myself desire to attach any other 
value to our results than a statistical one. Terrestrial magnetism is far from 
being able to dispense with such statistical work. In too many instances is 
this method the only one by which we can hope to improve the empirical 
basis upon which our theoreiical investigations must at present rest. 



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ABSTRACTS AND REVIEWS ' 



Hann, J. Die Er deals Games, ihre Attnosphare und Hydrosphare. Fiinfte 

neubearbeitete Auflage. Roy. 8vo. Prag. Wien. Leipzig, 1896. Pp. 336. 

24 colored plates and 92 diagrams. 

This volume forms Part I of the Fifth Edition of the well-known hand- 
book "Allgemeine Erdkunde," by Hann, Hochstetter, and Pokorny. Retaining 
practically the same excellent arrangement as its predecessors, it is much en- 
larged and, from a typographical point of view, much more attractive. Some 
of the chapters have been rewritten, and many illustrations have been added. 
No one is better qualified to prepare a trustworthy handbook in climatology 
than the veteran climatologist, Dr. Hann. The student of this subject will 
find in this volume a concise and clear presentation of the principles under- 
lying climate and weather, embodying the latest and best researches. The 
book is well suited to form the basis of a course of instruction in climatology 
in our colleges and universities. 

Containing, as it does, the latest results of study, it forms a valuable sup- 
plement to the " Handbuch der Klimatology," issued by the same author in 
1883, and which has ever since maintained its place as the standard text-book 
on climatology. The welcome announcement is made that a second edition 
of the " Handbuch," revised and enlarged, is now in press and will soon be 
issued. O. h. Fassig. 



BIBLIOTHECA GEOGRAPHICAL 



As long ago as 1853 the Berlin Gesellschaft Jur Erdkunde inaugurated the 
custom of giving a brief review of geographical literature in its Zeitschri/t. 
This was continued without interruption until the close of 1890 

The absence of the accustomed section in the Zeitschri/t for 1891, 1892, 
and 1893, devoted to a review of recent literature, called forth much complaint 
from members of the Society. In 1894 the Society decided to revive and 
greatly extend this bibliographic work. In place of devoting the last num- 
ber of the Zeitschri/t to a review of the literature for the current year, as 
heretofore, an annual volume is to be issued under the title, Bibliotheca 
Geographica, to be devoted exclusively to a classified catalogue of the geo- 
graphical publications of the year. 

The important work of compiling and editing this volume has been in- 
trusted to Herr Otto Baschin, of the scientific staff of the Prussian Meteor- 
ological Institute, a sufficient guarantee that this most exacting and volumi- 
nous work will be well done. 

Some idea of the wide range of topics included may be gathered from 
the table of contents: Under "General Geography" we find the divisions of 
Bibliography, Methodology and Instruction, Reference-books, Historical Geog- 

'Herausgegeben von der Gesellschaft fur Erdkunde zu Berlin. Bearbeitet von 
Otto Baschin. 8vo. Berlin. Kuhl. 

159 



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160 ABSTRACTS AND REVIEWS [vol. ii, no. 4 J 

raphy, Mathematical and Astronomical Geography, Physical Geography (in- 
cluding Climatolgy, Oceanology, and Terrestrial Magnetism), Biological Geo- 
graphy, Anthropo-geography, Travelers' Guides. Under the term "Special 
Geography " the division of titles is in accordance with continental areas 
and natural or political subdivisions. The entries contain full bibliograph- 
ical details of author's name, title, place, and date of publication, size, num- 
ber of pages, publisher, and in many instances the price. 

Volume I, issued in 1895, contains over 13,000 titles, comprising the geo- 
graphical literature of 1891 and 1892. Volumes II and III, issued in 1896 
and 1897, respectively contain about 10,000 titles each. By far the most of these 
titles are taken from periodicals and the serial publications of scientific so- 
cieties, of which over 800 have been indexed. These figures will convey some 
idea of the magnitude of the work undertaken by Mr. Baschin by authority 
of the Berlin Gesellsc haft fur Erdkunde. 

All who have occasion to refer to the literature of the wide range of sub- 
jects comprised within these volumes are placed under obligations to the So- 
ciety and the editor for this most excellent guide to the vast and rapidly 
growing mass of geographical literature. O. L. Fassig. 



THE BOUNDARY MONUMENTS OF THE DISTRICT OF COLUMBIA. 1 

[Abstract.] 

The earliest landmarks of the District of Columbia are the stone monu- 
ments which mark its boundaries. Of these there were forty originally, all 
located and erected in 1791 and 1792. After the protracted debate over the 
location of the seat of government of the very young United States was 
ended, and selection made of a tract not to exceed ten miles square on the 
banks of the Potomac, the tract was surveyed, and marked by Major Andrew 
Ellicott in 1791 and 1792. Major Ellicott being interested in the "variation 
of the compass," had the amonnt of observed variation carved on every oue 
of the monuments planted by him. To his intelligent interest we are doubt- 
less indebted for our earliest knowledge of the magnetic declination in the 
District of Columbia. Unfortunately the field notes of the survey can not be 
found, and it does not appear that Major Ellicott's values have ever been pub- 
lished. Hence, he who wished to make use of the information carved on the 
monuments had to get it, at first hand, by a forty-mile tramp across the 
fields in the outskirts of Washington. 

Mr. Marcus Baker, of the United States Geological Survey, who was at 
one time director of the Los Angeles Magnetic Observatory, has spent some 
of his leisure time, during the past three years, in hunting up the old monu- 
ments, and has published the results of his visits in this interesting pamphlet. 
He has thus performed a most valuable service. 

The original District of Columbia was a square, with each side cutting the 
meridian at an angle of 45 . Thus we have a N., E., S., W. corner, and also a 
S.W., N. W., N. E., and S. E. side. Throughout the entire extent of the forty- 
mile boundary, stone posts were set at every mile, thus making in all forty. 

»By Marcus Bakkr. Records of the Columbia Historical Society, vol. 1, pp. 
21,5-224. Washington, May, 1897. 15X23 cm. PI. 1. 



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ABSTRACTS AND REVIEWS 



161 



These stones are of the same material as that used in the first public buildings 
of Washington, known as freestone, and came from Aquia Creek in Virginia- 
They are about four feet long, two feet being in the rough and in the ground, 
and two feet above ground. The part above is one foot square and two feet 
high, with beveled top, forming the frustum of a four-sided pyramid. They 
were not dressed, but sawed out, as their surfaces show. Each of the four 
faces bears an inscription. The face fronting Virginia or Maryland bears the 
name Virginia or Maryland respectively. The opposite face, however, does 
not bear the name "District of Columbia," but in bold capitals the words, 
JURISDICTION OF THE UNITED STATES, and hence these stones are 
spoken of as "jurisdiction stones." 

The survey was begun April 15, 1791, and the stones on the Virginia line 
bear the date 1791 ; all others, 1792. Of these monuments, Mr. Baker found 
3 in very good condition ; 5 in good condition ; 16 in fair condition ; 9 in bad 
condition ; 3 had their tops broken off; 2 were wholly lost and site unmarked; 
and 2 in place, but invisible. He calls attention to the importance of pre- 
serving these monuments. For future reference, the author gives a full de- 
scription of each monument as taken from his field notes, and gives the fol- 
lowing tabular summary of the values of the " variation of the compass." 
The first thirteen monuments (S. to N. W. 3 inclusive) are on the Virginia 
line, and, as stated, these bear the date 1791, while all the others the date 
1792. These thirteen stones no longer mark the boundary of the District of 
Columbia, as that part of the original tract lying on the Virginia side of the 
Potomac was ceded back to Virginia in 1846. The blanks or question-marks 
occurring in the table are due to illegibility of the original marking. 



Summary of Variation of Compass Observed in 1791 or 1792, and Re- 
corded on the Boundary Monuments of the District of 
Columbia. 




4? W 



Stone 


1 
Var. || Stone 


Var. 


N 


i'VPE 1 


1 E 




o° io' E 


NE 1 


1 06 E, 


SE 


1 


11 E 


NE 2 


1 12 E 1 


|SE 


2 


04 E 


NE 3 


18 W 


■ SE 


-\ 


08 W 


NE 4 


25 W 


SE 


4 





NE 5 


22 E 


|SE 


5 


21 E 


NE 6 


51 E 


>SE 


6 


18 E 


NE 7 


1 08 E 1 


|SE 


7 


25 E 


NE 8 


24 E 


SE 


8 


34 E 


NE 9 


19 E 


,SE 


9 


37 E 



It will be seen that the values are quite irregular at times, the distances 
between the stones being only about a mile. While a part of these irregu- 
larities may be due to the instrumental means employed, nevertheless it is 
quite possible that they represent an actual fact, since distribution of the 
earth's magnetism in the vicinity of Washington, as shown by the magnetic 
survey of Maryland, is quite irregular. 



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RECEX T PUB LIC A TIOSS ' 



ALDtrcH, Wm. E. The Engineering Value of Magnetic Surveys. Jour, of As- 
sociation of Engineering Societies. May, 1S97. Pp. 304-3136. 15 x 22 an. 
[Abstract of paper presented at Annual Meeting of the Association. Jamt- 

Bacer, L. A. First report npon Magnetic Work in Maryland, including the 
History and Objects of Magnetic Surreys. Baltimore, 1S97. Special Pub- 
lication Maryland Geological Surrey." Vol. L Pt. V. iS,S x 26 cm 
Pp. 405-530. PL4- 

va* Bexxelex. W. Werte der erdmagnetiscben Declination fur die Periode 
1 500- 1 700, und ihrer Sacular~ Variation fur die Periode 1500-1S30. Kgi. Akad. 
van Wetenscbappen te Amsterdam. Verslag van de Gewone Vergadering 
der Wis-en Natuurkundige Afdeeling van 27 Februari. 1807. 18 x 26 cm. 
Pp. 390-400. [The author presents in a tabular form the values of the 
magnetic declination for various intersections of parallels of latitude and 
meridians for the epoch 1500-1700, as resulting from his latest researches. 
The isogonic charts, which will supersede his well-known former ones, 
will doubtless be published later. Tables of the secular variation for the 
epoch 1500-1850 are likewise given.] 

van Bemmelen, W. Nieuwe aanwinsten voor de verzameling van oude mis- 
wijzings-waarnemingen Kgl. Akad. van Wetenscbappen te Amsterdam. 
Repr. Verslag van de Gewone Vergadering der Wis-en Natuurkundige 
Afdeeling 27, November, 1897. 18 x 26 cm. Pp. 317-321. 

von Bezold, W. Zur Theorie des Erdmagnetismus. Sitz. ber. d. Akad. d. 
Wiss. zu Berlin, 1897, XVIII. 17^ x 25 cm. Pp. 414-449. PI. 2. [The 
present communication consists of two parts. The first deals with the 
fundamental principles of Gauss's General Theory of the Earth's Mag- 
netism especially as referring to the comparison of the results from 
theory with those of experiment. In the second part these principles are 
applied to an investigation of the diurnal variation.] 

Bigelow, F. H. The standard system of co-ordinate axes for magnetic and 
meteorological observations and computations. Repr. from Monthly 
Weather Review, May, 1897. Weather Bureau Bull. No 124. Washington, 
1897. Pp. 7. 15 x 22 cm. 

Eschenhagbn, M. Werthe der erdmagnetischen Elemente zu Potsdam fur 
das Jahr, 1896. Repr. Wied. Ann. Bd. 61. Pp. 411-413. 1897. 

Fwtsche, H. Ueber die Bestimmung der Coefficienten der Gaussischen Allge- 
meinen Theorie des Erdmagnetismus fur das Jahr, 1885, und iiber den 
Zusammenhang der drei erdmagnetischen Elemente untereinander. St. 
Petersburg, 1897. Pp. 85. 15^ x 23 cm. 



Observations magnetiques sur 509 lieux. Faites en Asie et en Europe 

pendant la periode de 1867-1894. Avec 3 Cartes des anomalies magne- 
tiques pres de Ioussar-oe de Moscou. St. Petersburg, 1897. i\% x 12% 
cm. Pp.41, PI. 3. 

» Not as yet otherwise noticed in the Journal. As the conventional sizes of 
publications vary so considerably, it has been decided to give the actual outside di- 
mensions, viz., the breadth and length, the former being given first. 
162 



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RECENT PUBLICATIONS 163 

Geelmuyden, H. Nogle Magnetiske Observationer i Nordmarken og i 
Christiania. Christiania, 1897. 15 x 22 cm. Pp 19. PI. 1. 

HarTl, Heinrich. Meteorologische und Magnetische Beobachtungen in 
Griechenland. Wien, 1895. Repr. from " Mittheilungen des K. u. K. 
militar-geographischen Institutes," XIV. Band. 15 x 23 cm. Pp. 56. 
PI. 5. [First Report; no magnetic results.] 

. Meteorol. u. Magn. Beob. in Griechenland. 2. Bericht. Wien, 1897. 

15x23 cm. Pp. 32. PI. 1. [Second report; pp. 5-32 give account of 
magnetic work at seven stations in Greece.] 

Hellmann, G., Die Anfange der Magnetischen Beobachtungen. Repr. from 
Zeitschrift der Gesellschaft fur Erdkunde zu Berlin. Berlin, 1897. XXXII. 
Band, Heft 2. 19 x 16 cm. Pp. 27. 

Hepites, ST. C. Analele Institutului Meteorologic al Rom&niei. Tomul XI 
Anul 1895. Boucarest and Paris, 1896. [Contains no magnetic work.] 

Ki,ossovsky, A. Revue M6t6orologique. Travaux du Roseau m£teorologique 
du sud-ouest de la Russie. Dix ans d' existence 1886-1895. Odessa, 1896. 

. Annales de l'Observatoire Magn6tique et M6t6orologique de 

TUniversite Imperiale a Odessa pour 1896. Odessa, 1897. [Pp. 8-57: 
Aufstellung der erdmagtietischen Variationsapparate im Magnetischen 
und Meteorologischen Observatorium der Kaiserl. Universitat in Odessa 
von Ernst Leyst und Paul Passalsky. PI. 1. Marche diurne des elements 
magn£tiques a Odessa. PI. 2. Jours de perturbations magneliques.] 

Lenz. Die Ergebnisse der magnetischen Beobachtungen in Bochum im 
Jahre 1896. Repr. from "Gliickauf," Berg-und Hiittenmannische Wochen- 
schrift, 1897, No. 14, und Beilage. 21^ x 28 cm. Pp. 13, PI. 2. 

Littlehales, G. W. Contributions to Terrestrial Magnetism. The Mag- 
netic Dip or Inclination, as observed at thirty important maritime sta- 
tions, together with an investigation of the seculiar chauge in the direc- 
tion of a freely suspended magnetic needle at twenty- nine of the stations. 
Hydrographic Office Publication, No. 114, Washington, 1897. 15 x 23 cm. 
Pp. 45. [One chart showing the secular change in the direction of a 
magnetic needle.] 

Lyman, B. S. Compass variation affected by geological structure in Bucks 
and Montgomery counties, Pennsylvania. Jour. Frauklin Institute, Oct., 
x 897- I 5 x 22 cm ' Pp* 281-284. One map. 

Moos, N. A. F. Report to the Secretary to Government General Department, 
Bombay. Pp. 13. [On the condition and proceedings of the Government 
Observatory, Col&ba, for year ending with 31st March, 1897.] 

Palazzo, L. Misure di magnetismo terrestre fatte in Sicilia nel 1890. Es- 
tratto dagli Annali dell' Ufficio Centrale Meteorologico e Geodinamico 
Vol. XVIII, parte 1, 1896, Roma, 1897. 24 x 34 cm. Pp. 102. 

Potsdam. Ergebnisse der magnetischen Beobachtungen im Jahre 1894. 

1894, Heft II. Veroffentlichungen des K. Preuss. Meteorologischen 

Instituts. Herausg. durch W. von Bezold. Berlin 1897. 26 x 34 cm. 

Pp. 44, PL 4- 
. Ergebnisse der magnetischen Beobachtungen im Jahre 1895. 1895, 

Heft II. Berlin 1897. 26 x 34 cm. Pp. 44, PI. 4. 

Putnam, G. R. The Scientific Work of the Boston Party on the Sixth Peary 
Expedition to Greenland. Report A. Magnetic and Pendulum obser- 
vations. Repr. from Technology Quarterly, Boston, Vol. X, No. 1, March, 
1897. 17 x 26 cm. Pp. 56-132. [For results of magnetic observations 
see Terr. Mag., March, 1897. Pp. 32.] 



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164 RECENT PUBLICATIONS [vol. ii, no. 4 .j 

Rykatchew, M. Annales de L'Observatoire Physique Central. Annee 1895. 
1 Partie. Observations meleorologiaues et magnltiques des stations de r 
ordre, observations extraordinaires des stations de 2 ordre et observations 
des stations de 3 ordre. St. Petersbourg, 1896. [I. Observations faites a 
robservatoire magne'tique et mlteorologique de Constantin a Pavlovsk 
pendant Tan nee 1895. Pp. XLIII — 146, III. Observations me'teorolog- 
lques et magne'tiques faites a TObservatoire d'Ekateriubourg pendant 
l'annee 1895. Pp. xii -•- 18. IV. Observations meteorologiques et ma§- 
netiques faites a TObservatoire d'Irkoutsk pendant Tannee 1595. Pp. xii 
-f 20.] 

Schmidt, A., (Gotha.) Ueber die Nothwendigkeit einer Vervollstandigung 
des Netzes der erdmagnetischen Observatorien. Repr. Beitrage zur 
Geophysik, Bd. Ill, Heft 2, 1897. 14 x 22 cm. Pp. 225-246. [Abstract in 
Terr. Mag., March, '97.] 

Van der Stok. Observations made at the Magnetical and Meteorological 
Observatory at Batavia. Vol. XVIII, 1895. [Meteorological and magnet- 
ical observations made during the year 1895, and results of meteoro- 
logical observations made during the years, 1 866-1895.] Batavia, 1896. 

United States Naval Observatory. Report of the Superintendent for 
the year ending June 30, 1894. Report of the Secretary of the Navy, 
1894. Pp. 164-169, Washington, 1895. 14 x 23 cm. 

. Report of Supt. for year ending June 30, 1897, Washington, 1897. 

14 x 23 cm. [The reports of the Superintendent of the Naval Observa- 
tory for 1895 and 1896 were published in the Reports of the Secretary of 
the Navy for those y ears - They have not been and probably will not be 
issued separately. These reports contain but brief accounts of the oper- 
ations of the Naval Observatory, and no observations or abstracts of 
results.] 



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